in reply to How to get a better error message from LWP::UserAgent on missing SSL certificates?
noxxi has written some tools for checking and debugging SSL connections. In his talk about debugging SSL, he especially recommends analyze-ssl.pl.
For those who prefer spoken word over text, there also is a live talk by Steffen Ullrich on debugging SSL/TLS from the GPW 2015.
In Section Seekers of Perl Wisdom