In a previous post I spoke about setting up the SSL cert for mail, but the web interface also needs SSL set up. The steps are actually similar, but without the extra bit for mail.
Here's what I did to fix it, just make sure you replace the example with your own domain. If you aren't running as root, use these commands otherwise put sudo in front of them all:
ln -s /home/admin/conf/web/ssl.example.com.pem /usr/local/vesta/ssl/certificate.crt ln -s /home/admin/conf/web/ssl.example.com.key /usr/local/vesta/ssl/certificate.key
If that didn't do the trick, restart apache and vestacp and it will now work with your new cert :)