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Magneto-optical Kerr-effect (MOKE) measurements of superconducting films with soft-magnetic coatings are performed at low temperatures using a laser-based MOKE set-up. An elaborate measurement scheme with internal reference allows the quantitative comparison of the temperature dependent Kerr-amplitude with the magnetic field generated by supercurrents. For this purpose, an amorphous CoFeB thin film exhibiting a large Kerr-signal is deposited directly on top of the YBCO superconductor acting as field sensing layer. It is shown that the resulting magnetic hysteresis loops of the soft-magnetic film can be used to reconstruct the electric properties of the superconductor.