I can vouch for LEMs, being used frequently in industrial equipment.
If you need higher accuracy, a special purpose CT (current transducer, that is) might be suitable, maybe one of those that works by magnetic saturation (VAC and a few others make them). Otherwise, for best results, you'll need a shunt, and an analog isolator or full on digitization (e.g., an ADC on the high side with SPI over optos).
Tim