Microsoft Live Custom Domains are now shutting down. I have been using this service for e-mail hosting for all my Microsoft Azure Websites, but now it is gone and no viable repl
I have found the same problem myself.
The only alternative in the past would have been to use Google's equivalent service, but they have also stopped it.
Realistically, there isn't a free answer to using custom domains with emails that I am aware of. Both Microsoft and Google offer paid for services, but cost per user/mailbox, per-year - compared to their free services this is a big jump in price.
Google charge £33 per user/mailbox, per year. Microsoft are slightly dearer at £39 per user/mailbox, per year, but include access to online versions of Office for each user too.
For my situation, the Microsoft route may be the better option, based on my customer preferences but I am sure that the Google service is equally adequate.
Hope this helps. (But let me know if you find a better alternative!!!)