I'm looking for a simple & reliable way to host a HTTPS enabled static page on a domain I own. The fist thing that came to mind was S3 static website hosting but there seems to be no way to enable HTTPS for that.
What other alternatives are there?
SSL certificates are issued to the domain it then requires installing via your host or yourself. Shared hosting, the host would do the install for you since you don't normally have the option to do so. On unmanaged services such as dedicated, vps and instances on Amazon you are expected to install software yourself.
Valid SSL certificates are issued by trusted ca companies these normally cost money, once you paid they issue you several unique files this are installed within the OS and not the top level... hence you won't the option since this is your responsibility as a unmanaged service.
So because they are issued to the domain and not the host and require installing is among many reasons they do not provide SSL on hosting. You will need to use a instance and install the ssl, or use a managed vps service or shared hosting if you don't want to install yourself.