An electronic device may include a display formed at a front face and a backside circuitry module formed at a rear face that opposes the front face. The backside circuitry module may be surrounded by coil structures and may be aligned with a protrusion in a rear wall housing at the rear face. The backside circuitry module may include a substrate to which sensor components or other components may be mounted. In particular, sensor circuitry, sensors, transceiver circuitry, connector circuitry, etc. may be mounted to the substrate. Antenna structures may be embedded within the substrate along with conductive paths for the sensor components and other components mounted to the substrate. Support structures in the backside circuitry module may support the substrate, sensor components, and other components. If desired, antenna structures may be formed on the support structures.