You can find the serial number in Swing Catalyst Main Menu > Hardware > Settings > Sensor Plate > Configure > Stance sensor tab.
Balance Plate serial number is on the bottom side of the plate.
Motion Plate 4 serial number is written on the MeasureX/SensorEdge box with four flat ribbon cables and a single USB cable.
Motion Plate 5 serial number is on the bottom side of the white Balance Plate, sitting on top of the gray force plate.