An electronic device may include one or more low-noise pressure sensors for measuring air pressure. The electronic device may include wireless communications circuitry for communicating with external devices also having pressure sensors. Pressure data gathered by an external device may be used as reference pressure data for the electronic device. For example, if both devices are located in the same building, both pressure sensors will detect similar pressure fluctuations due to doors opening and closing and temperature-control systems turning on and off. By subtracting the reference pressure data from the pressure data gathered by the electronic device, calibrated pressure data may be obtained and may be used to reliably detect vertical displacement changes of the electronic device. In other scenarios, the pressure data may be compared with the reference pressure data to determine whether the two devices are in the same room.