Assume that I have a host handling mydomain.com and I also have that host pointing mydomain2.com to a subdirectory.

What if I want SSL?

I know I can get a certificate for mydomain.com and it would work for whenever the user surfs and what is shown at the top of the browser is www.mydomain.com.

But can I also get a certificate for mydomain2.com and it would work for whenever the user surfs and what is shown at the top of the browser is www.mydomain2.com?

In other words can I have two certificates used on my site since there are two domain names?

Thanks in advance.

Each SSL site requires a dedicated IP address, so unless your host wants to provide you with a second IP for the second domain, no.

Yes, as mentioned your current host would need to delegate one more IP for the other certificate site- and that should not be a problem as SSL is a good reason for providing a new IP.