An electrosurgical instrument for delivering microwave electromagnetic energy into biological tissue, the instrument comprising: a coaxial cable for conveying microwave EM energy, the coaxial cable having an inner conductor, an outer conductor, and a first dielectric material separating the inner conductor and the outer conductor; and a radiating tip portion disposed at a distal end of the coaxial cable to receive microwave EM energy from the coaxial cable, the radiating tip portion comprising a second dielectric material different from the first dielectric material, wherein the radiating tip portion has an electrical length selected in conjunction with its dielectric properties at three or more frequencies of microwave EM energy to support resonance at the three or more frequencies of microwave EM energy, wherein the radiating tip is configured to deliver the microwave EM energy at the three or more frequencies, in an alternating or simultaneous manner, wherein the three or more frequencies of microwave EM energy comprise a first frequency, a second frequency that is lower that the first frequency, and a third frequency that is lower than the first frequency and the second frequency, and wherein the second dielectric material has a length approximately equal to: 2.5 wavelengths of the microwave EM energy at the first frequency in the second dielectric material; one wavelength of the microwave EM energy at the second frequency in the second dielectric material; and half a wavelength of the microwave EM energy at the third frequency in the second dielectric material. a coaxial cable for conveying microwave EM energy, the coaxial cable having an inner conductor, an outer conductor, and a first dielectric material separating the inner conductor and the outer conductor; and a radiating tip portion disposed at a distal end of the coaxial cable to receive microwave EM energy from the coaxial cable, the radiating tip portion comprising a second dielectric material different from the first dielectric material, wherein the radiating tip portion has an electrical length selected in conjunction with its dielectric properties at three or more frequencies of microwave EM energy to support resonance at the three or more frequencies of microwave EM energy, wherein the radiating tip is configured to deliver the microwave EM energy at the three or more frequencies, in an alternating or simultaneous manner, wherein the three or more frequencies of microwave EM energy comprise a first frequency, a second frequency that is lower that the first frequency, and a third frequency that is lower than the first frequency and the second frequency, and wherein the second dielectric material has a length approximately equal to: 2.5 wavelengths of the microwave EM energy at the first frequency in the second dielectric material; one wavelength of the microwave EM energy at the second frequency in the second dielectric material; and half a wavelength of the microwave EM energy at the third frequency in the second dielectric material. 2.5 wavelengths of the microwave EM energy at the first frequency in the second dielectric material; one wavelength of the microwave EM energy at the second frequency in the second dielectric material; and half a wavelength of the microwave EM energy at the third frequency in the second dielectric material.