An electronic device may contain wireless communication circuitry. The wireless communication circuitry may include radio-frequency transceiver circuitry coupled to multiple antennas. The electronic device may use the multiple antennas to make received signal power measurements. The signal power measurements may be made for each frequency in a list of frequencies used most recently by the electronic device in conveying data traffic between the electronic device and a wireless network. Based on received signal power measurements, the electronic device may select which frequency to use in performing system acquisition operations to attempt to establish a wireless communications link between the electronic device and the wireless network. The device may make signal power measurements for each antenna in the device to determine which antenna should be used in performing the system acquisition operations or may rotate through antennas in sequence to identify an antenna that can successfully perform system acquisition operations.