In a method and apparatus for shimming a superconducting magnet that has a number of magnet coils electrically connected in series between a first current connection and a second current connection and a superconducting switch connected in parallel with the magnet coils, between the first current connection and the second current connection, with the first current connection being electrically connected to an external current lead, a first solid-state switching device is electrically interposed between the external current lead and the magnet coils; a number of superconducting shim coils electrically connected between the first current connection and the second current connection through a further solid-state switching device. Superconducting switches are each connected in parallel with a respective superconducting shim coil.