An electrosurgical resection or dissection instrument (200, 300) for applying radiofrequency electromagnetic energy (EM) to a biological tissue, which has a first frequency, and microwave EM energy having a second frequency higher than the first frequency, the instrument comprising: a portable body (308) having an elongated probe element (306) extending therefrom, the probe element at its distal end having an instrument tip comprising a clamping mechanism having a pair of opposing fasteners (204, 206; 302, 304) that can be moved relative to each other between an open configuration to receive a biological vessel (214), e.g., a blood vessel, between them and a closed configuration for contacting the opposite sides of a received biological vessel, wherein one or both opposing fasteners includes an energy supply structure (212, 316) that c it comprises a body made of a first dielectric material (216, 318) and a first conductive element (218, 320) and a second conductive element (218, 322) that are separated by the first dielectric material; and a coaxial power cable (202, 314) connected to the portable body, the power cable comprising an internal conductor, an external conductor coaxial with the internal conductor and a second dielectric material that separates the external and internal conductors, the cable being configured of coaxial power to transmit to the portable body, simultaneously or separately, an RF signal having a first frequency and a microwave signal having a second frequency; wherein the inner conductor is electrically connected to the first conductor element or to each of them and the external conductor is electrically connected to the second conductor element or to each of them to allow one or both opposite surfaces (208, 210) of the tip of the The instrument independently emits the RF signal and the microwave signal, and where the first and second conductive elements are arranged on the opposite surface of the corresponding holding element to act: as a