Minutes after calling a livery car on a phone app, Lorena Cantillo easily picked out her ride in the crowd of black sedans on West 42nd Street. It was the only car with a pink sign in the window, and pink stickers all over the rear bumper.

“Good morning, Lorena,” called the driver, Martha Pitterson, 48, in a pink pashmina scarf, as she pulled up along the curb.

Ms. Cantillo’s ride was through a service that began Oct. 29 for New York City, Westchester County and Long Island and has navigated logistical and potential legal hurdles to match nearly 300 female drivers with passengers who request them through an app. Called SheTaxis — or SheRides in New York City, because of regulations prohibiting it from using “taxi” in its name — the service has received dozens of requests for rides and attracted a loyal following, even as it tries to sign on more female drivers in an industry dominated by men.

“There are times when I don’t want to get in a taxi because I’m alone and the man can be intimidating, especially if it’s nighttime and I’ve had too much to drink,” said Ms. Cantillo, 31, a makeup artist who booked her third ride with the service in a week.