A superconducting magnetic shielding system includes first and second planar superconducting shields respectively positioned above and below an environment to be shielded. The shields are each thermally coupled to a cold source at a respective thermalizing point. When the shields are cooled into the superconducting regime, they passively block magnetic fields via the Meissner Effect. Each shield may also be shaped to produce a smooth temperature gradient extending away from its thermalizing point; thus, as the shields are cooled, magnetic fields may be expelled away from the thermalizing point and, consequently, away from the environment to be shielded. A heater may also be provided opposite the thermalizing points to improve control of the temperature gradient.