A wireless power system may have a wireless power transmitting device and a wireless power receiving device. The wireless power receiving device may have a receive coil that receives wireless power signals from the wireless power transmitting device and may have a rectifier that produces direct-current power from the received wireless power signals. The wireless power transmitting device may have an array of transmit coils. Each transmit coil has a respective magnetic coupling coefficient characterizing its magnetic coupling with the receive coil. The wireless power transmitting device may have control circuitry that uses the magnetic coupling coefficient values in selecting transmit coils to use in transmitting wireless power to the wireless power receiving device.