A wireless power transmission system has a wireless power receiving device that is located on a charging surface of a wireless power transmitting device. The wireless power receiving device has a wireless power receiving coil and the wireless power transmitting device has a wireless power transmitting coil array. Signal measurement circuitry coupled to the coil array may make measurements while the control circuitry uses the inverter circuitry to apply excitation signals to each of the coils. Foreign objects on the coil array such as metallic objects without wireless power receiving coils can be detected using foreign object detection. When multiple wireless power receiving devices are present on the wireless power transmitting device, steps may be taken to isolate measurements from the coils associated with each wireless power receiving device. Foreign object detection may then be performed on these modified measurements.