An electrosurgical ablation apparatus for generating and emitting electromagnetic radiation energy for ablating biological tissue is disclosed. The apparatus comprises an operating unit (1), a handheld applicator unit (3) with an applicator antenna (4) and a cable connection (2) between both. The applicator antenna (4) is a dual or multi-resonant ablation antenna (41a, . . . 41d) for transmitting microwave ablation energy at at least two different frequencies which are selected especially according to the electrical properties and dimensions of the tissue to be ablated.