diff --git a/library/ssl_tls13_generic.c b/library/ssl_tls13_generic.c
index 4b027de..2104567 100644
--- a/library/ssl_tls13_generic.c
+++ b/library/ssl_tls13_generic.c
@@ -684,6 +684,18 @@
 #endif /* MBEDTLS_SSL_CLI_C */
     }
 
+    /*
+     * NONE means we skip all checks
+     *
+     * Note: we still check above that the server did send a certificate,
+     * because only a non-compliant server would fail to do so. NONE means we
+     * don't care about the server certificate being valid, but we still care
+     * about the server otherwise following the TLS standard.
+     */
+    if (authmode == MBEDTLS_SSL_VERIFY_NONE) {
+        return 0;
+    }
+
 #if defined(MBEDTLS_SSL_SERVER_NAME_INDICATION)
     if (ssl->handshake->sni_ca_chain != NULL) {
         ca_chain = ssl->handshake->sni_ca_chain;
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 3f64ef6..84342d5 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -5863,6 +5863,17 @@
 run_test    "Authentication: server badcert, client none" \
             "$P_SRV crt_file=$DATA_FILES_PATH/server5-badsign.crt \
              key_file=$DATA_FILES_PATH/server5.key" \
+            "$P_CLI debug_level=3 auth_mode=none" \
+            0 \
+            -C "x509_verify_cert() returned" \
+            -C "! The certificate is not correctly signed by the trusted CA" \
+            -C "! mbedtls_ssl_handshake returned" \
+            -C "send alert level=2 message=48" \
+            -C "X509 - Certificate verification failed"
+
+run_test    "Authentication: server badcert, client none (1.2)" \
+            "$P_SRV crt_file=$DATA_FILES_PATH/server5-badsign.crt \
+             key_file=$DATA_FILES_PATH/server5.key" \
             "$P_CLI force_version=tls12 debug_level=3 auth_mode=none" \
             0 \
             -C "x509_verify_cert() returned" \
@@ -5917,7 +5928,29 @@
             -C "X509 - Certificate verification failed" \
             -C "SSL - No CA Chain is set, but required to operate"
 
-# TODO: server goodcert, client none, no trusted CA
+requires_key_exchange_with_cert_in_tls12_or_tls13_enabled
+run_test    "Authentication: server goodcert, client none, no trusted CA" \
+            "$P_SRV" \
+            "$P_CLI debug_level=3 auth_mode=none ca_file=none ca_path=none" \
+            0 \
+            -C "x509_verify_cert() returned" \
+            -C "! The certificate is not correctly signed by the trusted CA" \
+            -C "! Certificate verification flags"\
+            -C "! mbedtls_ssl_handshake returned" \
+            -C "X509 - Certificate verification failed" \
+            -C "SSL - No CA Chain is set, but required to operate"
+
+requires_any_configs_enabled $TLS1_2_KEY_EXCHANGES_WITH_CERT
+run_test    "Authentication: server goodcert, client none, no trusted CA (1.2)" \
+            "$P_SRV" \
+            "$P_CLI force_version=tls12 debug_level=3 auth_mode=none ca_file=none ca_path=none" \
+            0 \
+            -C "x509_verify_cert() returned" \
+            -C "! The certificate is not correctly signed by the trusted CA" \
+            -C "! Certificate verification flags"\
+            -C "! mbedtls_ssl_handshake returned" \
+            -C "X509 - Certificate verification failed" \
+            -C "SSL - No CA Chain is set, but required to operate"
 
 # The purpose of the next two tests is to test the client's behaviour when receiving a server
 # certificate with an unsupported elliptic curve. This should usually not happen because