CiviMail recipient count stuck on Estimating
I was able to 'fix' the issue by simply deleting all the groups (I didn't have any previous mailings in here) from the Recipients field and then re-adding them. Make no other edits before the estimated number of recipients finishes, and the draft is saved. I was able to send a test email successfully after that. The mailing list this happened with to me is ~585 contacts.

NOTE: I just had this error pop up and found this Stack Exchange question from a Google search of the error message.