The Obstetrics Emergency Department is the first of its kind in Massachusetts.

When she felt the first contractions at 11:15 p.m. New Year’s Eve, Renai Townsend thought she had time to get to Boston to deliver her second child. “I thought they were Braxton Hicks contractions, which I had before,” she said. Renai called her parents to come over to watch her 2-year-old son, Will...