This post is older than a year. Consider some information might not be accurate anymore.
https://www.ssllabs.com/ provides a excellent detailed report about a SSL certificate. It not only checks the capability but also known vulnerabilities like Heartbleed. Another plus is that it has a simulation suite that tests the SSL handshake for several browsers or devices.
Qualys SSL Labs also maintains a collection of tools that are helpful in understanding SSL/TLS connections. One in particular is a View My Client page, which will display information about the client connection.
