I bought a commercial SSL certificate to use with my Zimbra install, and though I found it very straightforward to get it working with SMTP and Tomcat, I am struggling to get it working with my IMAP / POP daemons.
It was easy with Postfix/Tomcat because the procedures are widely documented, but since Zimbra uses home-grown IMAP/POP daemons, I have had trouble figuring it out.
Also, my server name is say server1.domain.com and my certificate is secure.domain.com (both pointing to the same IP). This seems to work fine with Tomcat and SMTP, but IMAPs AND POP3s are not even running (I'm assuming this because ports 993 and 995 are not listening on my box, while 110 and 143 are). And yes, SSL is turned on for both services in the admin tool.