Eddy current magnetic shielding by a rotating conductor has been utilized to create a low magnetic field region in the interior of a hollow cylinder. The enhancement of this effect by cooling to the superconducting state has been studied and applied to a superconducting device which easily generates and maintains an extremely low magnetic field region as a laboratory environment. The operation of certain commercial Hall probes at helium temperatures is discussed, and a novel method of measuring bulk resistivities as low as 10−14&OHgr;‐m is suggested.