An antenna may be formed from a peripheral conductive housing structure in an electronic device that is separated from an antenna ground by a gap. An antenna feed may be formed from a metal trace on a flexible printed circuit that spans the gap. The metal trace may have a line segment that joins a wider pad portion of the trace at a junction. A stiffener on the flexible printed circuit may have a protrusion that overlaps the junction. A metal bracket attached to the peripheral housing structure may be soldered to the pad. A metal member with meandering paths may form a return path in the antenna. The meandering path may have parallel segments that extend along an inner surface of the peripheral conductive housing structure to prevent the metal member from rotating when a screw is used to screw the metal member to the peripheral conductive housing structure.