Abstract: A primary superconductive magnetic field component or gradient pickup coil circuit is trimmed by means of one or more auxiliary superconductive trim coil circuits electromagnetically coupled to a magnetic flux sensor for sensing the magnetic flux coupled to the sensor by said primary and auxiliary coil circuits. The trim coils each have their respective magnetic axes oriented orthogonally for independent adjustment of trim. An adjustable magnetic shield is provided surrounding each of the respective trim coils for varying the coupling between the respective trim coil and the magnetic field. In this manner transverse and axial balance or trimming of the primary pickup coil circuit is obtained by adjusting the positions of the respective magnetic shields around each of the respective trim coil circuits. In a preferred embodiment, there are three mutually orthogonal trim coil circuits.