diff --git a/cmd/derper/cert.go b/cmd/derper/cert.go
index 623fa376f..b95755c64 100644
--- a/cmd/derper/cert.go
+++ b/cmd/derper/cert.go
@@ -4,16 +4,28 @@
 package main
 
 import (
+	"crypto/ecdsa"
+	"crypto/elliptic"
+	"crypto/rand"
+	"crypto/sha256"
 	"crypto/tls"
 	"crypto/x509"
+	"crypto/x509/pkix"
+	"encoding/json"
+	"encoding/pem"
 	"errors"
 	"fmt"
+	"log"
+	"math/big"
 	"net"
 	"net/http"
+	"os"
 	"path/filepath"
 	"regexp"
+	"time"
 
 	"golang.org/x/crypto/acme/autocert"
+	"tailscale.com/tailcfg"
 )
 
 var unsafeHostnameCharacters = regexp.MustCompile(`[^a-zA-Z0-9-\.]`)
@@ -65,8 +77,18 @@ func NewManualCertManager(certdir, hostname string) (certProvider, error) {
 	crtPath := filepath.Join(certdir, keyname+".crt")
 	keyPath := filepath.Join(certdir, keyname+".key")
 	cert, err := tls.LoadX509KeyPair(crtPath, keyPath)
+	hostnameIP := net.ParseIP(hostname) // or nil if hostname isn't an IP address
 	if err != nil {
-		return nil, fmt.Errorf("can not load x509 key pair for hostname %q: %w", keyname, err)
+		// If the hostname is an IP address, automatically create a
+		// self-signed certificate for it.
+		var certp *tls.Certificate
+		if os.IsNotExist(err) && hostnameIP != nil {
+			certp, err = createSelfSignedIPCert(crtPath, keyPath, hostname)
+		}
+		if err != nil {
+			return nil, fmt.Errorf("can not load x509 key pair for hostname %q: %w", keyname, err)
+		}
+		cert = *certp
 	}
 	// ensure hostname matches with the certificate
 	x509Cert, err := x509.ParseCertificate(cert.Certificate[0])
@@ -76,6 +98,18 @@ func NewManualCertManager(certdir, hostname string) (certProvider, error) {
 	if err := x509Cert.VerifyHostname(hostname); err != nil {
 		return nil, fmt.Errorf("cert invalid for hostname %q: %w", hostname, err)
 	}
+	if hostnameIP != nil {
+		// If the hostname is an IP address, print out information on how to
+		// confgure this in the derpmap.
+		dn := &tailcfg.DERPNode{
+			Name:     "custom",
+			RegionID: 900,
+			HostName: hostname,
+			CertName: fmt.Sprintf("sha256-raw:%-02x", sha256.Sum256(x509Cert.Raw)),
+		}
+		dnJSON, _ := json.Marshal(dn)
+		log.Printf("Using self-signed certificate for IP address %q. Configure it in DERPMap using: (https://tailscale.com/s/custom-derp)\n  %s", hostname, dnJSON)
+	}
 	return &manualCertManager{
 		cert:       &cert,
 		hostname:   hostname,
@@ -109,3 +143,69 @@ func (m *manualCertManager) getCertificate(hi *tls.ClientHelloInfo) (*tls.Certif
 func (m *manualCertManager) HTTPHandler(fallback http.Handler) http.Handler {
 	return fallback
 }
+
+func createSelfSignedIPCert(crtPath, keyPath, ipStr string) (*tls.Certificate, error) {
+	ip := net.ParseIP(ipStr)
+	if ip == nil {
+		return nil, fmt.Errorf("invalid IP address: %s", ipStr)
+	}
+
+	priv, err := ecdsa.GenerateKey(elliptic.P256(), rand.Reader)
+	if err != nil {
+		return nil, fmt.Errorf("failed to generate EC private key: %v", err)
+	}
+
+	serialNumberLimit := new(big.Int).Lsh(big.NewInt(1), 128)
+	serialNumber, err := rand.Int(rand.Reader, serialNumberLimit)
+	if err != nil {
+		return nil, fmt.Errorf("failed to generate serial number: %v", err)
+	}
+
+	now := time.Now()
+	template := x509.Certificate{
+		SerialNumber: serialNumber,
+		Subject: pkix.Name{
+			CommonName: ipStr,
+		},
+		NotBefore: now,
+		NotAfter:  now.AddDate(1, 0, 0), // expires in 1 year; a bit over that is rejected by macOS etc
+
+		KeyUsage:              x509.KeyUsageDigitalSignature | x509.KeyUsageKeyEncipherment,
+		ExtKeyUsage:           []x509.ExtKeyUsage{x509.ExtKeyUsageServerAuth},
+		BasicConstraintsValid: true,
+	}
+
+	// Set the IP as a SAN.
+	template.IPAddresses = []net.IP{ip}
+
+	// Create the self-signed certificate.
+	derBytes, err := x509.CreateCertificate(rand.Reader, &template, &template, &priv.PublicKey, priv)
+	if err != nil {
+		return nil, fmt.Errorf("failed to create certificate: %v", err)
+	}
+
+	certPEM := pem.EncodeToMemory(&pem.Block{Type: "CERTIFICATE", Bytes: derBytes})
+
+	keyBytes, err := x509.MarshalECPrivateKey(priv)
+	if err != nil {
+		return nil, fmt.Errorf("unable to marshal EC private key: %v", err)
+	}
+
+	keyPEM := pem.EncodeToMemory(&pem.Block{Type: "EC PRIVATE KEY", Bytes: keyBytes})
+
+	if err := os.MkdirAll(filepath.Dir(crtPath), 0700); err != nil {
+		return nil, fmt.Errorf("failed to create directory for certificate: %v", err)
+	}
+	if err := os.WriteFile(crtPath, certPEM, 0644); err != nil {
+		return nil, fmt.Errorf("failed to write certificate to %s: %v", crtPath, err)
+	}
+	if err := os.WriteFile(keyPath, keyPEM, 0600); err != nil {
+		return nil, fmt.Errorf("failed to write key to %s: %v", keyPath, err)
+	}
+
+	tlsCert, err := tls.X509KeyPair(certPEM, keyPEM)
+	if err != nil {
+		return nil, fmt.Errorf("failed to create tls.Certificate: %v", err)
+	}
+	return &tlsCert, nil
+}
diff --git a/cmd/derper/cert_test.go b/cmd/derper/cert_test.go
index a379e5c04..2ec7b756e 100644
--- a/cmd/derper/cert_test.go
+++ b/cmd/derper/cert_test.go
@@ -4,19 +4,29 @@
 package main
 
 import (
+	"context"
 	"crypto/ecdsa"
 	"crypto/elliptic"
 	"crypto/rand"
+	"crypto/sha256"
 	"crypto/tls"
 	"crypto/x509"
 	"crypto/x509/pkix"
 	"encoding/pem"
+	"fmt"
 	"math/big"
 	"net"
+	"net/http"
 	"os"
 	"path/filepath"
 	"testing"
 	"time"
+
+	"tailscale.com/derp"
+	"tailscale.com/derp/derphttp"
+	"tailscale.com/net/netmon"
+	"tailscale.com/tailcfg"
+	"tailscale.com/types/key"
 )
 
 // Verify that in --certmode=manual mode, we can use a bare IP address
@@ -95,3 +105,66 @@ func TestCertIP(t *testing.T) {
 		t.Fatalf("GetCertificate returned nil")
 	}
 }
+
+// Test that we can dial a raw IP without using a hostname and without a WebPKI
+// cert, validating the cert against the signature of the cert in the DERP map's
+// DERPNode.
+//
+// See https://github.com/tailscale/tailscale/issues/11776.
+func TestPinnedCertRawIP(t *testing.T) {
+	td := t.TempDir()
+	cp, err := NewManualCertManager(td, "127.0.0.1")
+	if err != nil {
+		t.Fatalf("NewManualCertManager: %v", err)
+	}
+
+	cert, err := cp.TLSConfig().GetCertificate(&tls.ClientHelloInfo{
+		ServerName: "127.0.0.1",
+	})
+	if err != nil {
+		t.Fatalf("GetCertificate: %v", err)
+	}
+
+	ln, err := net.Listen("tcp", "127.0.0.1:0")
+	if err != nil {
+		t.Fatalf("Listen: %v", err)
+	}
+	defer ln.Close()
+
+	ds := derp.NewServer(key.NewNode(), t.Logf)
+
+	derpHandler := derphttp.Handler(ds)
+	mux := http.NewServeMux()
+	mux.Handle("/derp", derpHandler)
+
+	var hs http.Server
+	hs.Handler = mux
+	hs.TLSConfig = cp.TLSConfig()
+	go hs.ServeTLS(ln, "", "")
+
+	lnPort := ln.Addr().(*net.TCPAddr).Port
+
+	reg := &tailcfg.DERPRegion{
+		RegionID: 900,
+		Nodes: []*tailcfg.DERPNode{
+			{
+				RegionID: 900,
+				HostName: "127.0.0.1",
+				CertName: fmt.Sprintf("sha256-raw:%-02x", sha256.Sum256(cert.Leaf.Raw)),
+				DERPPort: lnPort,
+			},
+		},
+	}
+
+	netMon := netmon.NewStatic()
+	dc := derphttp.NewRegionClient(key.NewNode(), t.Logf, netMon, func() *tailcfg.DERPRegion {
+		return reg
+	})
+	defer dc.Close()
+
+	_, connClose, _, err := dc.DialRegionTLS(context.Background(), reg)
+	if err != nil {
+		t.Fatalf("DialRegionTLS: %v", err)
+	}
+	defer connClose.Close()
+}
diff --git a/derp/derphttp/derphttp_client.go b/derp/derphttp/derphttp_client.go
index 7387b60b4..319c02429 100644
--- a/derp/derphttp/derphttp_client.go
+++ b/derp/derphttp/derphttp_client.go
@@ -652,7 +652,11 @@ func (c *Client) tlsClient(nc net.Conn, node *tailcfg.DERPNode) *tls.Conn {
 			tlsConf.VerifyConnection = nil
 		}
 		if node.CertName != "" {
-			tlsdial.SetConfigExpectedCert(tlsConf, node.CertName)
+			if suf, ok := strings.CutPrefix(node.CertName, "sha256-raw:"); ok {
+				tlsdial.SetConfigExpectedCertHash(tlsConf, suf)
+			} else {
+				tlsdial.SetConfigExpectedCert(tlsConf, node.CertName)
+			}
 		}
 	}
 	return tls.Client(nc, tlsConf)
@@ -666,7 +670,7 @@ func (c *Client) tlsClient(nc net.Conn, node *tailcfg.DERPNode) *tls.Conn {
 func (c *Client) DialRegionTLS(ctx context.Context, reg *tailcfg.DERPRegion) (tlsConn *tls.Conn, connClose io.Closer, node *tailcfg.DERPNode, err error) {
 	tcpConn, node, err := c.dialRegion(ctx, reg)
 	if err != nil {
-		return nil, nil, nil, err
+		return nil, nil, nil, fmt.Errorf("dialRegion(%d): %w", reg.RegionID, err)
 	}
 	done := make(chan bool) // unbuffered
 	defer close(done)
@@ -741,6 +745,17 @@ func (c *Client) dialNode(ctx context.Context, n *tailcfg.DERPNode) (net.Conn, e
 
 	nwait := 0
 	startDial := func(dstPrimary, proto string) {
+		dst := cmp.Or(dstPrimary, n.HostName)
+
+		// If dialing an IP address directly, check its address family
+		// and bail out before incrementing nwait.
+		if ip, err := netip.ParseAddr(dst); err == nil {
+			if proto == "tcp4" && ip.Is6() ||
+				proto == "tcp6" && ip.Is4() {
+				return
+			}
+		}
+
 		nwait++
 		go func() {
 			if proto == "tcp4" && c.preferIPv6() {
@@ -755,7 +770,6 @@ func (c *Client) dialNode(ctx context.Context, n *tailcfg.DERPNode) (net.Conn, e
 					// Start v4 dial
 				}
 			}
-			dst := cmp.Or(dstPrimary, n.HostName)
 			port := "443"
 			if !c.useHTTPS() {
 				port = "3340"
diff --git a/net/tlsdial/tlsdial.go b/net/tlsdial/tlsdial.go
index 2af87bd02..4d22383ef 100644
--- a/net/tlsdial/tlsdial.go
+++ b/net/tlsdial/tlsdial.go
@@ -12,6 +12,7 @@ package tlsdial
 import (
 	"bytes"
 	"context"
+	"crypto/sha256"
 	"crypto/tls"
 	"crypto/x509"
 	"errors"
@@ -246,6 +247,46 @@ func SetConfigExpectedCert(c *tls.Config, certDNSName string) {
 	}
 }
 
+// SetConfigExpectedCertHash configures c's VerifyPeerCertificate function
+// to require that exactly 1 cert is presented, and that the hex of its SHA256 hash
+// is equal to wantFullCertSHA256Hex and that it's a valid cert for c.ServerName.
+func SetConfigExpectedCertHash(c *tls.Config, wantFullCertSHA256Hex string) {
+	if c.VerifyPeerCertificate != nil {
+		panic("refusing to override tls.Config.VerifyPeerCertificate")
+	}
+	// Set InsecureSkipVerify to prevent crypto/tls from doing its
+	// own cert verification, but do the same work that it'd do
+	// (but using certDNSName) in the VerifyPeerCertificate hook.
+	c.InsecureSkipVerify = true
+	c.VerifyConnection = nil
+	c.VerifyPeerCertificate = func(rawCerts [][]byte, _ [][]*x509.Certificate) error {
+		if len(rawCerts) == 0 {
+			return errors.New("no certs presented")
+		}
+		if len(rawCerts) > 1 {
+			return errors.New("unexpected multiple certs presented")
+		}
+		if fmt.Sprintf("%02x", sha256.Sum256(rawCerts[0])) != wantFullCertSHA256Hex {
+			return fmt.Errorf("cert hash does not match expected cert hash")
+		}
+		cert, err := x509.ParseCertificate(rawCerts[0])
+		if err != nil {
+			return fmt.Errorf("ParseCertificate: %w", err)
+		}
+		if err := cert.VerifyHostname(c.ServerName); err != nil {
+			return fmt.Errorf("cert does not match server name %q: %w", c.ServerName, err)
+		}
+		now := time.Now()
+		if now.After(cert.NotAfter) {
+			return fmt.Errorf("cert expired %v", cert.NotAfter)
+		}
+		if now.Before(cert.NotBefore) {
+			return fmt.Errorf("cert not yet valid until %v; is your clock correct?", cert.NotBefore)
+		}
+		return nil
+	}
+}
+
 // NewTransport returns a new HTTP transport that verifies TLS certs using this
 // package, including its baked-in LetsEncrypt fallback roots.
 func NewTransport() *http.Transport {
diff --git a/tailcfg/derpmap.go b/tailcfg/derpmap.go
index 056152157..b3e54983f 100644
--- a/tailcfg/derpmap.go
+++ b/tailcfg/derpmap.go
@@ -139,6 +139,12 @@ type DERPNode struct {
 	// name. If empty, HostName is used. If CertName is non-empty,
 	// HostName is only used for the TCP dial (if IPv4/IPv6 are
 	// not present) + TLS ClientHello.
+	//
+	// As a special case, if CertName starts with "sha256-raw:",
+	// then the rest of the string is a hex-encoded SHA256 of the
+	// cert to expect. This is used for self-signed certs.
+	// In this case, the HostName field will typically be an IP
+	// address literal.
 	CertName string `json:",omitempty"`
 
 	// IPv4 optionally forces an IPv4 address to use, instead of using DNS.