I wish more applications would provide an easy way to use self-signed certs without totally compromising security.
Edit: link to davdroid issue: https://github.com/rfc2822/davdroid/issues/3
StartSSL's heart is in the right place but they're throttling the edge and very close to being ostracized completely.
see: cadroid.bitfire.at (it's free)
But it's a sign that support for self-signed certs is coming. Along with this pull request, that he just closed (not sure what the status is):
"When you first connect, it will show you a popup with a long set of characters. Check if it ends with A4FE and if so, click yes" is the very maximum I might be able to squeeze out of them. Manually importing a certificate in the trust store and dealing with the scary warnings ("Someone is monitoring your connection!") it generates is a no go.