Abstract: A proof mass support system has a pair of alignment coils for controlling the rest position of an elongate proof mass. The alignment coils are constructed to provide a levitation force when they carry electric currents which varies along the length of the proof mass. The relative strength of the electric currents are tuned in the alignment coils to cause the proof mass to take up a predetermined orientation with respect to one or more degrees of freedom defined by the alignment coils. In an alternative, one or more anti-rotation coils may be arranged to apply a restoring force to the proof mass when electric currents pass therethrough. The proof mass is formed so as to cooperate with the restoring force which acts against rotation of the proof mass away from a predetermined orientation. The system is typically provided as part of a superconducing accelerometer or gravity gradiometer.