I'd share a bunch of tools i use for test mail server setup.
SSL Certificate and TLS
First of all test if server establish ssl connections.
openssl s_client -connect mail.server.me:25 -starttls smtp
Next step is test TLS and check does certificate is valid with very handy tool:
DKIM, SPF checks
There is service to check mail authorization, simple send email to it:
echo "hi" | mail -s "testme" email@example.com
it should send results back to you then.
As well, there is more options such as extracting gmail headers information and so on, listed methods above is enough in my case.