Methods and apparatus are provided for verifying proper operation of a gas turbine engine output torque sensor using a speed sensor, and using the speed sensor as a backup torque sensor. Gas turbine engine output torque is sensed using a reference torque sensor, and gas turbine engine output shaft rotational speed is sensed. Gas turbine engine output torque is calculated from the sensed gas turbine engine output shaft rotational speed. The sensed gas turbine engine output torque is compared to the calculated gas turbine engine output torque to determine if the reference torque sensor is operating properly. The gas turbine engine is controlled at least partially based on the sensed gas turbine engine output torque if the reference torque sensor is determined to be operating properly, and is controlled at least partially based on the calculated output torque if the reference torque sensor is determined to be not operating properly.