An electronic device may have a housing in which electrical components on a printed circuit board are mounted. A connector may be mounted to the edge of the printed circuit board using solder. The connector may have a threaded portion that protrudes through the housing. A threadless portion of the connector may be aligned with the housing. The connector may have a metal body member covered with a metal shell. The metal shell may have a portion that covers the electrical components and serves as an electromagnetic interference shield for the electrical components. The connector may have a threaded barrel. The threaded barrel may have a threaded outer portion with a diameter that is larger than a threaded inner portion. The threadless portion of the connector may lie between the threaded outer and inner portions.