Present synchrotron light sources make extensive use of insertion devices like wigglers, undulators or wavelength-shifters. Among these, undulators are the most advanced sources for the generation of synchrotron radiation. The photons generated by a single electron add up coherently along the electron trajectory. In order to do so the oscillatory motion of the electron has to be in phase with the emitted photons along the whole undulator. Small magnetic errors can cause unwanted destructive interferences. In standard permanent magnet undulators the magnetic errors are reduced by applying shimming techniques. Superconductive undulators have higher magnetic fields than permanent magnet undulators but shimming is more complex. In this talk a novel passive shimming method based on superconductive closed loops is presented. It is shown that coupled superconductive loops installed along the surface of the superconductive undulator coil can significantly reduce the destructive effect of the field errors. The concept was verified by a proof of principle experiment.