I\'m setting up a webserver for a system that needs to be used only through HTTPS, on an internal network (no access from outside world)
I did the following, which worked nicely for me:
I got a wildcard SSL cert for *.mydomain.com (Namecheap, for example, provide this cheaply)
I created a CNAME DNS record pointing "mybox.mydomain.com" at "mybox.local".
I hope that helps - unfortunately you'll have the expense of a wildcard cert for your domain name, but you may already have that.