We are building an apparatus for Earth-based testing of a gyroscope system to be used in a satellite test of general relativity. The immediate goal is a readout capable of measuring the direction of the gyroscope spin axis to an angular resolution of one arcsecond over a limited range. A combination of SQUID magnetometers and persistent current loops are used to measure the London moment of the spinning superconducting rotor levitated electrostatically. To obtain a trapped flux signal in the gyroscope sufficiently smaller than the London moment signal, the apparatus makes use of a new magnetic field shielding technique for obtaining large superconductor shielded regions below 10-7gauss.