CC supports HTTPS, but only using a URL, for example https://foo.bar.com/. If the URL doesn't specify a port then 443 is used.
The reason CC requires a URL is that SSL certificate verification (almost always) requires a host name, not an IP address. CC does not support self-signed certificates. Actually, it is better to say that the underlying http library (apache) doesn't support self-signed certs without a bunch of extra work that I am not interested in doing.
To summarize the setup: to use HTTPS you must:
- Get a DNS name for your calibre content server: dynamic or static, paid or free.
- Setup your calibre server so that the DNS name opens the server. How you do this depends on where the server is located on the 'net and what routers are between you and that server. You can use calibre's url prefix if needed (calibre preferences).
- Get an SSL domain validation certificate, paid or free such as from https://letsencrypt.org/
- Set up calibre (calibre preferences) to use the certificate, or set up a web server using the certificate to be a reverse proxy front end for calibre.
- (Optionally) Set up calibre to use usernames and passwords
- Test using a web browser that you can access the content server using HTTPS, and that usernames work if you are using them.
- Enter the URL for the calibre server into CC (Settings / Connecting to calibre / content server connection) using something like https://your.domain.name. You don't need to add the port if it is using the standard 443. Check the box saying that "The IP box contains a complete URL". Check the "Allow connecting using 3G" if you intend to access the server using cell technology.