A superconducting self-shielding three-solenoid system with an adjustable shielding factor is developed, implemented, and characterized using a single antiproton in a Penning trap. With the tuned system, we suppress external magnetic field disturbances by up to a factor of 225 ± 15, allowing antiproton-toproton charge-to-mass ratio comparisons with fourfold reduced frequency fluctuations and antiproton magnetic moment determinations with tenfold reduced uncertainty.