The security scanning tool nmap has a scripting library as part of it.
There is a "ssl-enum-ciphers" script that ships in the standard nmap builds that tests a device for which TLS/SSL versions it supports, and which cipher suites it supports.
nmap --script ssl-enum-ciphers -p 443 1.2.3.4
Would help you understand both the versions and ciphers a web server supports
