An electronic device may have components mounted in a housing. The device may include wireless transceiver circuitry and antenna structures. A display may be mounted in the housing. The display may have a cover layer having an inner surface with a recess. The recess may run along a peripheral edge of the cover layer. An antenna structure such as an inverted-F antenna resonating element may be formed from a metal trace on a dielectric antenna carrier. The resonating element may be mounted in the recess without adhesive. Conductive vias may pass through the dielectric carrier. Metal members with dimples may be soldered to a flexible printed circuit and may be used to ground metal traces on the carrier and the flexible printed circuit to the housing when the carrier is attached to the housing with fasteners.