A wireless power system has a wireless power transmitting device and a wireless power receiving device. The wireless power transmitting device uses a wireless power transmitting coil to transmit wireless power signals to the wireless power receiving device during wireless power transmission periods. During alternating foreign object detection periods, the wireless power transmitting device gathers signals from the wireless power transmitting coil to detect foreign objects. Another wireless power transmitting device may transmit signals that can cause interference. To help reduce interference, the wireless power transmitting device gathers signals with a sensing coil that is separate from the wireless power transmitting coil and subtracts these signals from signals gathered with the wireless power transmitting coil. A signal quality metric may be used in adjusting the timing of the foreign object detection periods to help avoid interference from the other wireless power transmitting device.