FastMail has released their Calendar feature and contact synchronisation is coming very soon now.
You can get access to it from https://mail.ferguson.pw/calendar, or by clicking your name in the top left corner (1) and then selecting calendar (2) from the drop down menu:
Your account may need to be upgraded to “Enhanced” if you want to sync your calendar with another program or device, such as Outlook, OSX Calendar.app, Android, or iPhone. If you are wanting to sync, please let me know so we can get you setup. Once enabled, you can follow these instructions: https://www.fastmail.fm/help/clients/applist.html
Additional help can be found at: https://www.fastmail.fm/help/#calendar or by sending me an email.