Abstract: An electromagnetic medical applicator for tissue-heating comprises a single resonant element (1) in contact with one surface of a layer of material (5) whose opposite surface faces the body of a patient (6). The material has a wave-impedance which approximately matches that of the human body and a dielectric constant not less than for a material having unity magnetic permeability which produces this match. In one form the element is a patch resonator (1) on a substrate (2) backed by a ground-plane (3) and overlaid by the layer (5); at least the substrate may include both dielectric and magnetic material in order to combine a desired resonator size-reduction and wave-impedance. In another form a needle-type applicator is coated with the layer of material.