Abstract: A coupling structure for coupling two resonant cavities, which may be dissimilar, based on providing a metallic surface, called here a guide surface, at an angle intermediate between the orientation of the magnetic field in the two cavities. The guide surface may be one surface of a non-rectangular window cut in a wall separating the two cavities or may be the surface of a coupling screw piercing, at the intermediate angle, a rectangular window in a wall between the two cavities. In the non-rectangular window embodiment, an adjusting tuning screw is provided that screws into a notch in the guide surface. In the angled coupling screw embodiment, coupling is adjusted by providing that more or less of the angled coupling screw extends into the rectangular window. The coupling structure couples any two cavities having mutually orthogonal magnetic fields by providing the guide surface at an orientation so the magnetic field in each cavity has a non-zero projection onto the guide surface.