Для тех, кому нужна версия Swift от @Jeff Thompson:
// Get a current time for where you want to start measuring from
var date = NSDate()
// do work...
// Find elapsed time and convert to milliseconds
// Use (-) modifier to conversion since receiver is earlier than now
var timePassed_ms: Double = date.timeIntervalSinceNow * -1000.0
Надеюсь, это поможет вам.