We present details of the design and construction of a new superconducting, magnetically suspended torsion balance in which the levitation coil and the lift surface of the float lie on the surfaces of concentric spheres. We compare results from calculations of the variation of the inductance with the levitated height and transverse motion of the float with experimental measurements and show that the levitation system is stable. Angular motion of the torsion balance is detected using superconducting pick-up coils whose inductance is modulated by float rotation. The subsequent change in current flowing in the persistent circuit containing the coils is measured using a flux-gate magnetometer. The pick-up coils exert a restoring torque on the float which can be modified by adjusting the persistent current stored. Periods down to 60 s should be obtainable for a current of 2.5 A. Preliminary results of ring-down experiments in He gas at a pressure of 53Pa show that periods of angular oscillations of 24 s with quality factor, Q, of about 200 can be obtained. The moment of inertia of the float is 2 × 10-5 kg m2. The observed period of 24 s indicates that there is an additional restoring torque in the system which may be due to trapped flux. The observed value of Q is consistent with gas damping.