diff --git a/ssl/test/runner/alert.go b/ssl/test/runner/alert.go
index 541216e..7db6826 100644
--- a/ssl/test/runner/alert.go
+++ b/ssl/test/runner/alert.go
@@ -22,6 +22,7 @@
 	alertRecordOverflow         alert = 22
 	alertDecompressionFailure   alert = 30
 	alertHandshakeFailure       alert = 40
+	alertNoCertficate           alert = 41
 	alertBadCertificate         alert = 42
 	alertUnsupportedCertificate alert = 43
 	alertCertificateRevoked     alert = 44
diff --git a/ssl/test/runner/common.go b/ssl/test/runner/common.go
index 42f4a00..74c552e 100644
--- a/ssl/test/runner/common.go
+++ b/ssl/test/runner/common.go
@@ -473,6 +473,10 @@
 	// NewSessionTicket message despite promising to in ServerHello.
 	SkipNewSessionTicket bool
 
+	// SkipClientCertificate causes the client to skip the Certificate
+	// message.
+	SkipClientCertificate bool
+
 	// SkipChangeCipherSpec causes the implementation to skip
 	// sending the ChangeCipherSpec message (and adjusting cipher
 	// state accordingly for the Finished message).
diff --git a/ssl/test/runner/conn.go b/ssl/test/runner/conn.go
index 5a19c28..fe0b139 100644
--- a/ssl/test/runner/conn.go
+++ b/ssl/test/runner/conn.go
@@ -856,7 +856,7 @@
 // L < c.out.Mutex.
 func (c *Conn) sendAlert(err alert) error {
 	level := byte(alertLevelError)
-	if err == alertNoRenegotiation || err == alertCloseNotify {
+	if err == alertNoRenegotiation || err == alertCloseNotify || err == alertNoCertficate {
 		level = alertLevelWarning
 	}
 	return c.SendAlert(level, err)
diff --git a/ssl/test/runner/handshake_client.go b/ssl/test/runner/handshake_client.go
index 1f52dce..67609fc 100644
--- a/ssl/test/runner/handshake_client.go
+++ b/ssl/test/runner/handshake_client.go
@@ -564,15 +564,20 @@
 	hs.writeServerHash(shd.marshal())
 
 	// If the server requested a certificate then we have to send a
-	// Certificate message, even if it's empty because we don't have a
-	// certificate to send.
+	// Certificate message in TLS, even if it's empty because we don't have
+	// a certificate to send. In SSL 3.0, skip the message and send a
+	// no_certificate warning alert.
 	if certRequested {
-		certMsg := new(certificateMsg)
-		if chainToSend != nil {
-			certMsg.certificates = chainToSend.Certificate
+		if c.vers == VersionSSL30 && chainToSend == nil {
+			c.sendAlert(alertNoCertficate)
+		} else if !c.config.Bugs.SkipClientCertificate {
+			certMsg := new(certificateMsg)
+			if chainToSend != nil {
+				certMsg.certificates = chainToSend.Certificate
+			}
+			hs.writeClientHash(certMsg.marshal())
+			c.writeRecord(recordTypeHandshake, certMsg.marshal())
 		}
-		hs.writeClientHash(certMsg.marshal())
-		c.writeRecord(recordTypeHandshake, certMsg.marshal())
 	}
 
 	preMasterSecret, ckx, err := keyAgreement.generateClientKeyExchange(c.config, hs.hello, leaf)
diff --git a/ssl/test/runner/handshake_server.go b/ssl/test/runner/handshake_server.go
index 0232772..d2cac98 100644
--- a/ssl/test/runner/handshake_server.go
+++ b/ssl/test/runner/handshake_server.go
@@ -626,13 +626,22 @@
 	// certificate message, even if it's empty.
 	if config.ClientAuth >= RequestClientCert {
 		var certMsg *certificateMsg
-		if certMsg, ok = msg.(*certificateMsg); !ok {
+		var certificates [][]byte
+		if certMsg, ok = msg.(*certificateMsg); ok {
+			if c.vers == VersionSSL30 && len(certMsg.certificates) == 0 {
+				return errors.New("tls: empty certificate message in SSL 3.0")
+			}
+
+			hs.writeClientHash(certMsg.marshal())
+			certificates = certMsg.certificates
+		} else if c.vers != VersionSSL30 {
+			// In TLS, the Certificate message is required. In SSL
+			// 3.0, the peer skips it when sending no certificates.
 			c.sendAlert(alertUnexpectedMessage)
 			return unexpectedMessageError(certMsg, msg)
 		}
-		hs.writeClientHash(certMsg.marshal())
 
-		if len(certMsg.certificates) == 0 {
+		if len(certificates) == 0 {
 			// The client didn't actually send a certificate
 			switch config.ClientAuth {
 			case RequireAnyClientCert, RequireAndVerifyClientCert:
@@ -641,14 +650,16 @@
 			}
 		}
 
-		pub, err = hs.processCertsFromClient(certMsg.certificates)
+		pub, err = hs.processCertsFromClient(certificates)
 		if err != nil {
 			return err
 		}
 
-		msg, err = c.readHandshake()
-		if err != nil {
-			return err
+		if ok {
+			msg, err = c.readHandshake()
+			if err != nil {
+				return err
+			}
 		}
 	}
 
diff --git a/ssl/test/runner/runner.go b/ssl/test/runner/runner.go
index 4c46639..52729e3 100644
--- a/ssl/test/runner/runner.go
+++ b/ssl/test/runner/runner.go
@@ -2656,6 +2656,28 @@
 			})
 		}
 	}
+
+	testCases = append(testCases, testCase{
+		testType:      serverTest,
+		name:          "RequireAnyClientCertificate",
+		flags:         []string{"-require-any-client-certificate"},
+		shouldFail:    true,
+		expectedError: ":PEER_DID_NOT_RETURN_A_CERTIFICATE:",
+	})
+
+	testCases = append(testCases, testCase{
+		testType: serverTest,
+		name:     "SkipClientCertificate",
+		config: Config{
+			Bugs: ProtocolBugs{
+				SkipClientCertificate: true,
+			},
+		},
+		// Setting SSL_VERIFY_PEER allows anonymous clients.
+		flags:         []string{"-verify-peer"},
+		shouldFail:    true,
+		expectedError: ":TLS_PEER_DID_NOT_RESPOND_WITH_CERTIFICATE_LIST:",
+	})
 }
 
 func addExtendedMasterSecretTests() {
@@ -2859,12 +2881,37 @@
 	// TLS client auth.
 	tests = append(tests, testCase{
 		testType: clientTest,
-		name:     "ClientAuth-NoCertificate",
+		name:     "ClientAuth-NoCertificate-Client",
 		config: Config{
 			ClientAuth: RequestClientCert,
 		},
 	})
 	tests = append(tests, testCase{
+		testType: serverTest,
+		name:     "ClientAuth-NoCertificate-Server",
+		// Setting SSL_VERIFY_PEER allows anonymous clients.
+		flags: []string{"-verify-peer"},
+	})
+	if protocol == tls {
+		tests = append(tests, testCase{
+			testType: clientTest,
+			name:     "ClientAuth-NoCertificate-Client-SSL3",
+			config: Config{
+				MaxVersion: VersionSSL30,
+				ClientAuth: RequestClientCert,
+			},
+		})
+		tests = append(tests, testCase{
+			testType: serverTest,
+			name:     "ClientAuth-NoCertificate-Server-SSL3",
+			config: Config{
+				MaxVersion: VersionSSL30,
+			},
+			// Setting SSL_VERIFY_PEER allows anonymous clients.
+			flags: []string{"-verify-peer"},
+		})
+	}
+	tests = append(tests, testCase{
 		testType: clientTest,
 		name:     "ClientAuth-NoCertificate-OldCallback",
 		config: Config{