https (ssl secured) local websites are not working in Safari and Chrome in Mac Yosemite. How can I fix this?
It's likely that the issue is with certificates for your server.  You probably don't have a SSL certificate for localhost:8443 (as it's unlikely that any CA is going to issue one for that hostname), so of course you're going to get certificate errors.  Either click through the certificate errors; or choose a valid domain that you control, get a certificate for it, and host your site on that domain.

If you have a certificate for your domain (example.com) and you have a SSL certificate for that domain (e.g., for www.example.com), another thing you could try is setting up DNS (or your /etc/hosts file) so that www.example.com resolves localhost (127.0.0.1).  This still might run into other issues, and really, it's better to just test it on the domain you have a certificate for or click through the certificate errors.

None of this is likely to be Mac OS X specific.