This invention relates mainly to methods and apparatus for magnetizing a superconductor. We describe a method of changing the magnetization of a superconductor, by automatically controlling a magnet to generate a wave of magnetic flux, in particular a standing wave of magnetic flux, adjacent to the surface of said superconductor. In preferred implementations of the method the superconductor is positioned within a magnetic circuit including a ferromagnetic or ferrimagnetic material and the method further comprises regulating the magnetic circuit during or after changing the superconductor's magnetization.