I test quite a few electric motors and use a clip-on ammeter connected to my vibration meter to check for broken rotor bars if the motor is in service. The motor needs to be at a high load for broken bars to show correctly. I have found that there needs to be slip side band frequencies on both sides of the line frequency to be sure broken rotor bars are present, not just one side band frequency on the lower side and the amplitude of the side bands needs to be above a certain level.
Rewind shops can test for broken bars with various methods but the motor needs to be out of service.
Probably the most comon way is to supply 2 phases to the stator winding and rotate the rotor slowly by hand and check the current deflection. The best method I know of is to feed high current into the shaft from a transformer. The shaft will act as a primary winding and the bars act as the secondary. Heat will build up at high resistance joints which is extremely easily picked up using an infrared camera. If it's bad you will feel the temperature rise with your hand.