@example
$ gnutls-cli-debug localhost
GnuTLS debug client 3.5.0
Checking localhost:443
                             for SSL 3.0 (RFC6101) support... yes
                        whether we need to disable TLS 1.2... no
                        whether we need to disable TLS 1.1... no
                        whether we need to disable TLS 1.0... no
                        whether %NO_EXTENSIONS is required... no
                               whether %COMPAT is required... no
                             for TLS 1.0 (RFC2246) support... yes
                             for TLS 1.1 (RFC4346) support... yes
                             for TLS 1.2 (RFC5246) support... yes
                                  fallback from TLS 1.6 to... TLS1.2
                        for RFC7507 inappropriate fallback... yes
                                     for HTTPS server name... Local
                               for certificate chain order... sorted
                  for safe renegotiation (RFC5746) support... yes
                     for Safe renegotiation support (SCSV)... no
                    for encrypt-then-MAC (RFC7366) support... no
                   for ext master secret (RFC7627) support... no
                           for heartbeat (RFC6520) support... no
                       for version rollback bug in RSA PMS... dunno
                  for version rollback bug in Client Hello... no
            whether the server ignores the RSA PMS version... yes
whether small records (512 bytes) are tolerated on handshake... yes
    whether cipher suites not in SSL 3.0 spec are accepted... yes
whether a bogus TLS record version in the client hello is accepted... yes
         whether the server understands TLS closure alerts... partially
            whether the server supports session resumption... yes
                      for anonymous authentication support... no
                      for ephemeral Diffie-Hellman support... no
                   for ephemeral EC Diffie-Hellman support... yes
                    ephemeral EC Diffie-Hellman group info... SECP256R1
                  for AES-128-GCM cipher (RFC5288) support... yes
                  for AES-128-CCM cipher (RFC6655) support... no
                for AES-128-CCM-8 cipher (RFC6655) support... no
                  for AES-128-CBC cipher (RFC3268) support... yes
             for CAMELLIA-128-GCM cipher (RFC6367) support... no
             for CAMELLIA-128-CBC cipher (RFC5932) support... no
                     for 3DES-CBC cipher (RFC2246) support... yes
                  for ARCFOUR 128 cipher (RFC2246) support... yes
                                       for MD5 MAC support... yes
                                      for SHA1 MAC support... yes
                                    for SHA256 MAC support... yes
                              for ZLIB compression support... no
                     for max record size (RFC6066) support... no
                for OCSP status response (RFC6066) support... no
              for OpenPGP authentication (RFC6091) support... no
@end example

You could also use the client to debug services with starttls capability.
@example
$ gnutls-cli-debug --starttls-proto smtp --port 25 localhost
@end example