For more than a year, federal authorities pursued a man they called simply "the Hacker." Only after using a little known cellphone-tracking device—a stingray—were they able to zero in on a California home and make the arrest.

Stingrays are designed to locate a mobile phone even when it's not being used to make a call. The Federal Bureau of Investigation considers the devices to be so critical that it has a policy of deleting the data gathered in their use, mainly to keep suspects in the dark about their capabilities,...