An electronic device may have wireless circuitry with antennas. An antenna may have an inverted-F antenna resonating element, an antenna ground, and other resonating element structures. A tip of the antenna resonating element and the antenna ground may be separated by a peripheral housing gap filled with plastic. The antenna may be sensitive to capacitance changes induced by the presence of a user's hand overlapping the gap or other portions of the antenna. A hand capacitance sensing electrode may be mounted in the plastic of the gap or elsewhere in the vicinity of the antenna. A transmission line may couple the hand capacitance sensing electrode to the antenna to retune the antenna in the event that the user's hand overlaps the antenna.