diff --git a/jetforce_diagnostics.py b/jetforce_diagnostics.py
index 8ffa8a8..efa831a 100755
--- a/jetforce_diagnostics.py
+++ b/jetforce_diagnostics.py
@@ -11,6 +11,7 @@ should be taken with a grain of salt and analyzed on their own merit.
 import argparse
 import contextlib
 import datetime
+import ipaddress
 import socket
 import ssl
 import sys
@@ -122,7 +123,8 @@ class BaseCheck:
         proto = socket.IPPROTO_TCP
         addr_info = socket.getaddrinfo(host, port, family, type_, proto)
         if not addr_info:
-            raise UserWarning("No address found for host")
+            raise UserWarning(f"No {family} address found for host")
+        # Gemini IPv6
         return addr_info[0][4]
 
     @contextlib.contextmanager
@@ -193,8 +195,10 @@ class IPv6Address(BaseCheck):
     def check(self) -> None:
         log(f"Looking up IPv6 address for {self.args.host!r}")
         addr = self.resolve_host(socket.AF_INET6)
-        if addr[0].startswith("::ffff:"):
-            raise UserWarning("Found an IPv4-mapped address, skipping check")
+        if ipaddress.ip_address(addr[0]).ipv4_mapped:
+            raise UserWarning(
+                "Found IPv4-mapped address, is your network IPv6 enabled?"
+            )
         log(f"{addr[0]!r}", style="success")
         log(f"Attempting to connect to [{addr[0]}]:{addr[1]}")
         with socket.socket(socket.AF_INET6, socket.SOCK_STREAM) as sock:
@@ -225,12 +229,17 @@ class TLSClaims(BaseCheck):
 
     def check(self) -> None:
         try:
+            # $ pip install cryptography
+            import cryptography
             from cryptography.hazmat.backends import default_backend
-            from cryptography.x509.oid import NameOID
+            from cryptography.x509.oid import NameOID, ExtensionOID
         except ImportError:
-            raise UserWarning("Could not import cryptography library, skipping")
+            raise UserWarning("cryptography library not installed, skipping check")
 
         with self.connection() as sock:
+            # Python refuses to parse a certificate unless the issuer is validated.
+            # Because many gemini servers use self-signed certs, we need to use
+            # a third-party library to parse the certs from their binary form.
             der_x509 = sock.getpeercert(binary_form=True)
             cert = default_backend().load_der_x509_certificate(der_x509)
             now = datetime.datetime.utcnow()
@@ -243,11 +252,33 @@ class TLSClaims(BaseCheck):
             style = "success" if cert.not_valid_after >= now else "failure"
             log(f"{cert.not_valid_after} UTC", style)
 
-            log("Checking common name matches hostname")
-            cn = cert.subject.get_attributes_for_oid(NameOID.COMMON_NAME)[0].value
-            cert_dict = {"subject": ((("commonName", cn),),)}
+            log("Checking subject claim matches server hostname")
+            subject = []
+            for cn in cert.subject.get_attributes_for_oid(NameOID.COMMON_NAME):
+                subject.append(("commonName", cn.value))
+
+            subject_alt_name = []
+            try:
+                ext = cert.extensions.get_extension_for_oid(
+                    ExtensionOID.SUBJECT_ALTERNATIVE_NAME
+                )
+            except cryptography.x509.ExtensionNotFound:
+                pass
+            else:
+                for dns in ext.value.get_values_for_type(cryptography.x509.DNSName):
+                    subject_alt_name.append(("DNS", dns))
+                for ip_address in ext.value.get_values_for_type(
+                    cryptography.x509.IPAddress
+                ):
+                    subject_alt_name.append(("IP Address", ip_address))
+
+            cert_dict = {
+                "subject": (tuple(subject),),
+                "subjectAltName": tuple(subject_alt_name),
+            }
+            log(f"{cert_dict!r}", style="info")
             ssl.match_hostname(cert_dict, self.args.host)
-            log(repr(cn), style="success")
+            log(f"Hostname {self.args.host!r} matches claim", style="success")
 
 
 class TLSVerified(BaseCheck):
@@ -274,14 +305,18 @@ class TLSRequired(BaseCheck):
 
     def check(self) -> None:
         log("Sending non-TLS request")
-        with socket.create_connection((self.args.host, self.args.port)) as sock:
-            sock.sendall(f"gemini://{self.netloc}\r\n".encode())
-            fp = sock.makefile("rb")
-            header = fp.readline().decode()
-            if header:
-                log(f"Received unexpected response {header!r}", style="failure")
-            else:
-                log(f"Connection closed by server", style="success")
+        try:
+            with socket.create_connection((self.args.host, self.args.port)) as sock:
+                sock.sendall(f"gemini://{self.netloc}\r\n".encode())
+                fp = sock.makefile("rb")
+                header = fp.readline().decode()
+                if header:
+                    log(f"Received unexpected response {header!r}", style="failure")
+                else:
+                    log(f"Connection closed by server", style="success")
+        except Exception as e:
+            # A connection error is a valid response
+            log(f"{e}", style="success")
 
 
 class ConcurrentConnections(BaseCheck):
@@ -547,7 +582,7 @@ class URLSchemeMissing(BaseCheck):
     """A URL without a scheme should be inferred as gemini"""
 
     def check(self) -> None:
-        url = f"://{self.netloc}/\r\n"
+        url = f"//{self.netloc}/\r\n"
         response = self.make_request(url)
 
         log("Status should be 20 (SUCCESS)")
@@ -591,6 +626,8 @@ class URLDotEscape(BaseCheck):
         log(f"{response.status!r}", style)
 
 
+# TODO: Test sending a transient client certificate
+# TODO: Test with client pinned to TLS v1.1
 CHECKS = [
     IPv4Address,
     IPv6Address,