A microwave device for the ablation of biological tissues including a coaxial antenna, including an internal conductor, surrounded by a layer of dielectric material, an external conductor coaxial to the dielectric metal tip electrically connected to the internal conductor, and a quarter wave impedance transformer including a sleeve made of dielectric material having a proximal end covered with a layer of metal, the metal extending over nearly a quarter wavelength of electromagnetic field in the dielectric at the operating frequency of the device or of odd multiples of the quarter wavelength, the layer of metal material being connected electrically to the external conductor.