a medical fastening device for an electromagnetic sensor with a clamping element and with a sensor mount and to a medical device with such a fastening device, with an electromagnetic sensor and with a medical instrument. The clamping element has a counterpiece and a pressing piece movable relative to the clamping element, wherein the counterpiece has a lateral opening, which frees a free mounting area, which is itself at least partially enclosed by the counterpiece in a frame-like manner. The counterpiece has a depression, which points towards the mounting area and is arranged opposite the pressing piece, wherein the counterpiece is provided with an opening arranged opposite the depression. The pressing piece is movable in the opening in the direction of the depression of the counterpiece.