A month before their baby’s due date, Brad Hoylman and David Sigal got a call from the woman they had hired to have their child.

She was having contractions; come right away.

Mr. Sigal, a filmmaker, had the more flexible schedule. So after a sleepless night, he hopped on a plane to San Diego while Mr. Hoylman stayed in New York and frantically oversaw the dusty conversion of their TV room into a nursery.

The contractions turned out to be a false alarm, but Mr. Sigal stayed. And stayed, touching up his documentary in his hotel room, going to family outings — a picnic, a cheerleading event — with the surrogate and her daughters, and calling Mr. Hoylman “every 10 minutes” with updates.

Four weeks later, the baby was induced, and Mr. Hoylman flew in for the birth.

‘The timing was perfect,” Mr. Hoylman said. “I cut the cord and David —”