Owncloud 9.1.1-1.2 and Davdroid (1.3.1-ose) CalDAV-CardDAV

The important part you can test is to open:

http://example.com/.well-known/caldav

and:

http://example.com/.well-known/carddav

in your browser. After you get asked for your username and password there you need to be redirected to a page stating something like:

This is the WebDAV interface. It can only be accessed by WebDAV clients such as the ownCloud desktop sync client.

If that is working it might be possible that your *DAV interface / setup is not working completely / fully. For that we have a FAQ thread available (especially the litmus part there can help you to check your environment):