New York matchmaker Amy Van Doran looks like fashion designer Edna Mode from The Incredibles, only she’s a few decades younger and her bobbed hair is not black but bright orange. Working out of a storefront in the East Village, Van Doran’s job is to find love for a client list made up exclusively of women—most in their 40s—who each pay upwards of $15,000 for an entry in her vintage Rolodex.

It sounds like a stereotype 40 years out of date. And yet Van Doran is in high demand. More than that, she’s considered cool. “When I first started out, matchmaking was something people were a little embarrassed about,” she says. “Now I’m being invited to weddings, and people are telling their friends they’re working with me.”

Van Doran is walking through the East Village wh...