diff --git a/ssl/handshake_client.cc b/ssl/handshake_client.cc
index a99f87e..de5d8e9 100644
--- a/ssl/handshake_client.cc
+++ b/ssl/handshake_client.cc
@@ -1350,6 +1350,7 @@
 
   uint16_t signature_algorithm;
   if (!tls1_choose_signature_algorithm(hs, &signature_algorithm)) {
+    ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_HANDSHAKE_FAILURE);
     return ssl_hs_error;
   }
   if (ssl_protocol_version(ssl) >= TLS1_2_VERSION) {
diff --git a/ssl/handshake_server.cc b/ssl/handshake_server.cc
index 48005b1..3ecba37 100644
--- a/ssl/handshake_server.cc
+++ b/ssl/handshake_server.cc
@@ -861,6 +861,7 @@
     // Determine the signature algorithm.
     uint16_t signature_algorithm;
     if (!tls1_choose_signature_algorithm(hs, &signature_algorithm)) {
+      ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_HANDSHAKE_FAILURE);
       return ssl_hs_error;
     }
     if (ssl_protocol_version(ssl) >= TLS1_2_VERSION) {
diff --git a/ssl/test/runner/runner.go b/ssl/test/runner/runner.go
index 53f6ac8..b296260 100644
--- a/ssl/test/runner/runner.go
+++ b/ssl/test/runner/runner.go
@@ -2812,7 +2812,7 @@
 			messageCount:            5,
 			keyUpdateRequest:        keyUpdateRequested,
 			readWithUnfinishedWrite: true,
-			flags: []string{"-async"},
+			flags:                   []string{"-async"},
 		},
 		{
 			name: "SendSNIWarningAlert",
@@ -8644,12 +8644,14 @@
 				shouldVerifyFail = true
 			}
 
-			var signError, verifyError string
+			var signError, signLocalError, verifyError, verifyLocalError string
 			if shouldSignFail {
 				signError = ":NO_COMMON_SIGNATURE_ALGORITHMS:"
+				signLocalError = "remote error: handshake failure"
 			}
 			if shouldVerifyFail {
 				verifyError = ":WRONG_SIGNATURE_TYPE:"
+				verifyLocalError = "remote error"
 			}
 
 			suffix := "-" + alg.name + "-" + ver.name
@@ -8674,6 +8676,7 @@
 				tls13Variant:                   ver.tls13Variant,
 				shouldFail:                     shouldSignFail,
 				expectedError:                  signError,
+				expectedLocalError:             signLocalError,
 				expectedPeerSignatureAlgorithm: alg.id,
 			})
 
@@ -8702,9 +8705,10 @@
 				},
 				// Resume the session to assert the peer signature
 				// algorithm is reported on both handshakes.
-				resumeSession: !shouldVerifyFail,
-				shouldFail:    shouldVerifyFail,
-				expectedError: verifyError,
+				resumeSession:      !shouldVerifyFail,
+				shouldFail:         shouldVerifyFail,
+				expectedError:      verifyError,
+				expectedLocalError: verifyLocalError,
 			})
 
 			testCases = append(testCases, testCase{
@@ -8728,6 +8732,7 @@
 				},
 				shouldFail:                     shouldSignFail,
 				expectedError:                  signError,
+				expectedLocalError:             signLocalError,
 				expectedPeerSignatureAlgorithm: alg.id,
 			})
 
@@ -8755,9 +8760,10 @@
 				},
 				// Resume the session to assert the peer signature
 				// algorithm is reported on both handshakes.
-				resumeSession: !shouldVerifyFail,
-				shouldFail:    shouldVerifyFail,
-				expectedError: verifyError,
+				resumeSession:      !shouldVerifyFail,
+				shouldFail:         shouldVerifyFail,
+				expectedError:      verifyError,
+				expectedLocalError: verifyLocalError,
 			})
 
 			if !shouldVerifyFail {
diff --git a/ssl/tls13_both.cc b/ssl/tls13_both.cc
index 4424318..b9f5163 100644
--- a/ssl/tls13_both.cc
+++ b/ssl/tls13_both.cc
@@ -537,6 +537,7 @@
   SSL *const ssl = hs->ssl;
   uint16_t signature_algorithm;
   if (!tls1_choose_signature_algorithm(hs, &signature_algorithm)) {
+    ssl_send_alert(ssl, SSL3_AL_FATAL, SSL_AD_HANDSHAKE_FAILURE);
     return ssl_private_key_failure;
   }