Qualys SSL Labs also has a great online tool that allows you to quickly analyze your configuration changes [1]. Highly recommended and a great resource if you're just setting up your SSL certificate, too, to make sure you have it set correctly.
I've found that some of these will work with, e.g. Dovecot's IMAPS daemon, just by appending ":993" to the hostname.
Yesterday I found one that would only work on port 443, but it was a simple matter of creating two iptables rules: one to permit incoming IP packets to 443/TCP and the other to redirect them to 993/TCP.
Not to my knowledge; a full testing tool for IMAP, SMTP, TLS, DKIM, and DNSSEC would have been amazing a year or so ago when I was still maintaining mail servers!
[1] https://www.ssllabs.com/ssltest/analyze.html?d=news.ycombina...