During a recent audit, I had to harden the cipher suites used to secure a worldwide insurance application. The most important part of this task was to help adjust our customers, ensuring their infrastructure to be compatible with our future settings. During the whole project, I used different methods to double-check the settings applied to our differents tests and staging environments (packet analyzes, vulnerability scanner, etc.). I found out that Qualys, one of our security providers, has a free website that can scan a website and provide an interesting report:
https://www.ssllabs.com/ssltest/
There are a lot of similar services ( https://www.immuniweb.com/ssl/ for instance), with more or less the same functionality, but that one was particularly convenient to use.