So you heard about Fastmail's CardDav beta? Finding their setup page lacking?

So did I!

Taking a look at their servers and ports page (at the time of this writing) gave me the clues I needed. Try these settings with the "CardDav-sync beta" app:

Server	https://carddav.messagingengine.com/
SSL	Yes
Username	Your FastMail email address, including the domain
Password	Your FastMail password (probably want to create an alternative login)

That'll get you started. Now go have yourself some fun times syncing contacts.