Checking HTTPS setup on Apache/Nginx before using

There is a good Linux command line script testssl.sh you can use for this purpose. I've used this for other protocols as well (e.g. FTPS).

As as final check I will still use the SSL Server Test. It generates a pretty test result you can forward to customers ;-) .

You could make a copy of the config files and edit the ports. From there you could start a second instance of the webserver (nginx/apache) and check for valid configuration.
Instead of accessing https://www.your-domain.com (port 443) you change to https://www.your-domain.com:8443 (port 8443).
With a running instance you can check with external tools and check the logs for errors. This minimizes the risk that your website gets unavailable after config and certificate changes.
Depending on the size of your config and amount of vhosts this might be a very time consuming solution.

Solution also metioned in the comments by @symcbean.