After trying to upgrade our (very) old Tine 2.0 installation to the latest version of Tine 2.0, Tine 2.0 was not able to connect to our mailservers anymore. After testing a few things, it became clear that the PHP IMAP module had problems with the SSL certificate we are using for our mailservers. Even though it is not a self-signed certificate, imap_open() failed to connect to the mailserver. After digging a bit in the Tine 2.0 sources, I found that peer verification can be disabled by setting the peerVerify flag to false. Since I could not find a UI setting in the Tine 2.0 setup for this option, the solution was simple: Look for the imap configuration in the tine20_config database table and add the peerVerify:false setting to the existing JSON object for the connection configuration.
Disclaimer: Before trying this, understand the implications of this configuration. Disabling peer verification effectively means that the SSL certificates are ignored by the client, which is never a good idea. For a quick test on the local network this is "ok", for production usage it is not.