An electronic device may be provided with antenna structures and control circuitry. The antenna structures may include an antenna resonating element arm, an antenna ground, and an antenna feed coupled between the antenna resonating element arm and the antenna ground. The electronic device may include a tunable component configured to tune a frequency response of the antenna structures. The electronic device may also include a substrate, a radio-frequency transceiver on the substrate, control circuitry configured to generate control signals, a flexible printed circuit, and a connector. The connector may mechanically secure the flexible printed circuit to the substrate and may be electrically coupled to the transceiver and the control circuitry. The flexible printed circuit may include a radio-frequency transmission line coupled between the antenna feed and the connector and a control signal path coupled between the tunable component and the connector.