An electronic device such as a wristwatch may have a housing with metal portions such as metal sidewalls. The housing may form an antenna ground for an antenna. An antenna resonating element for the antenna may be formed from a stack of capacitively coupled component layers such as a display layer, touch sensor layer, and near-field communications antenna layer at a front face of the device. An additional antenna may be formed from a peripheral resonating element that runs along a peripheral edge of the device and the antenna ground. A rear face antenna may be formed using a wireless power receiving coil as a radio-frequency antenna resonating element or may be formed from metal antenna traces on a plastic support for light-based components.