It appears that Outlook 2011 (up to date with patches) will not receive mail from a server with a self-signed (and therefore not trusted) certificate. When I send mail I am prompted to trust it or not: This works, but when Outlook is quit and relaunched, the trusted state is forgotten (this might be a problem with Apple Keychain).  It's an annoyance, but at least I can send mail.

In receiving, I am not prompted at all, and no mail arrives. No error is written to the Errors window. Also, when sending or receiving, Outlook usually has a progress indicator in the lower right.  It's there for sending, but nothing happens at all when I click "send & receive" and there's nothing to send.

When I select Tools > IMAP Folders, the server appears on the left, but no folders appear on the right. (I can view them in Apple Mail.) I have compared my settings to a document I maintain of email server settings, and everything matches. The server does not use nonstandard port numbers.

And finally, I noted that when I view the settings in the Preferences window there is a yellow dot next to the server name. I'm assuming that yellow means a problem is indicated.