You can use OpenSSL and run this command:
openssl.exe s_client -connect www.mysite.com:443
which will use a generic SSL/TLS client to connect to your site and give you a ton of diagnostic info. You can see your entire SSL cert chain, the SSL handshake, SSL session info, etc. Here’s a full list of switches you can use with it: http://www.openssl.org/docs/apps/s_client.html
And here’s a great online tool to graphically verify your SSL chain is intact: http://www.sslshopper.com/ssl-checker.html
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