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Many experiments in nuclear and neutron physics are confronted with the problem that they use a superconducting magnetic spectrometer which potentially affects other experiments by their stray magnetic field. The retardation spectrometer aSPECT consists, inter alia, of a superconducting magnet system that produces a strong longitudinal magnetic field of up to 6.2T. In order not to disturb other experiments in the vicinity of aSPECT, we had to develop a magnetic field return yoke for the magnet system. While the return yoke must reduce the stray magnetic field, the internal magnetic field and its homogeneity should not be affected. As in many cases, the magnetic shielding for aSPECT must manage with limited space. In addition, we must ensure that the additional magnetic forces on the magnet coils are not destructive. In order to determine the most suitable geometry for the magnetic shielding for aSPECT, we simulated a variety of possible geometries and combinations of shielding materials of non-linear permeability. The results of our simulations were checked through magnetic field measurements both with Hall and nuclear magnetic resonance probes. The experimental data are in good agreement with the simulated values: The mean deviation from the simulated exterior magnetic field is (-1.7+/-4.8)%. However, in the two critical regions, the internal magnetic field deviates by 0.2% respectively <1E-4 from the simulated values.