A judge in Texas is raising questions about whether investigators are giving courts enough details on technological tools that let them get data on all the cellphones in an area, including those of innocent people.

In two cases, Magistrate Judge Brian Owsley rejected federal requests to allow the warrantless use of “stingrays” and “cell tower dumps,” two different tools that are used for cellphone tracking. The judge said the government should apply for warrants in the cases, but the attorneys had instead applied for lesser...