While a browser may be nice for viewing web pages, the command line may be even better for troubleshooting your SSL and TLS connections. These are the quick and dirty commands to connect to these types of sites. See the source below for a more detailed explanation.
openssl s_client -connect <sitename>:<port> ... GET / HTTP/1.0
TLS and SSL ports
gnutls-cli -s <sitename> -p <port>