I think you may have mixed up acronyms.
"IMAP Calendar" isn't a thing- IMAP is for E-mail- Internet Mail Access Protocol. It knows nothing of Calendar stuff (which is probably for the best)
MAPI, however does- MAPI is part of the Microsoft Exchange Protocol. Allegedly it is supported by the Mail Servers in Exchange, Axigen Mail Server, Kerio Connect, Scalix, Zimbra, HP OpenMail, IBM Lotus Notes, Zarafa, and Bynari, according to the MAPI Wikipedia article. (Exchange being pretty obvious, the others- I don't know. And I doubt any of those are free)