An electrosurgical resection or dissection instrument (200, 300) for applying to biological tissue radiofrequency electromagnetic energy having a first frequency and microwave EM energy having a second frequency higher than the first frequency, the instrument comprising: a handheld body having an elongate probe member extending therefrom, the probe member having at its distal end an instrument tip comprising a clamping mechanism having a pair of opposing clamping members (204, 206; 302, 304) that are movable relative to each other between an open configuration for receiving a biological vessel, e.g. a blood vessel, therebetween and a closed configuration for contacting opposite sides of a received biological vessel, wherein one or both of the opposing clamping members includes an energy delivery structure (212, 316) comprising a body made of a first dielectric material (216, 318), and a first conductive element (218, 320) and a second conductive element (218, 322) which are separated by the first dielectric material; and a coaxial feed cable (202, 314) connected to the handheld body, the feed cable comprising an inner conductor, an outer conductor coaxial with the inner conductor, and a second dielectric material separating the outer and inner conductors, the coaxial feed cable being configured for conveying to the handheld body, simultaneously or separately, an RF signal having the first frequency and a microwave signal having the second frequency; wherein the inner conductor is electrically connected to the or each first conductive element and the outer conductor is electrically connected to the or each second conductive element to enable one or both opposed surfaces (208, 210) of the instrument tip to emit independently the RF signal and the microwave signal, and wherein the first and second conductive elements are arranged at the opposed surface of the respective clamping member to act: as active and return electrodes to transfer RF EM energy into biological tissue by conduction from the respective clamping member, and as an antenna to radiate microwave EM energy into biological tissue from the opposed surface of the respective clamping member. a handheld body having an elongate probe member extending therefrom, the probe member having at its distal end an instrument tip comprising a clamping mechanism having a pair of opposing clamping members (204, 206; 302, 304) that are movable relative to each other between an open configuration for receiving a biological vessel, e.g. a blood vessel, therebetween and a closed configuration for contacting opposite sides of a received biological vessel, wherein one or both of the opposing clamping members includes an energy delivery structure (212, 316) comprising a body made of a first dielectric material (216, 318), and a first conductive element (218, 320) and a second conductive element (218, 322) which are separated by the first dielectric material; and a coaxial feed cable (202, 314) connected to the handheld body, the feed cable comprising an inner conductor, an outer conductor coaxial with the inner conductor, and a second dielectric material separating the outer and inner conductors, the coaxial feed cable being configured for conveying to the handheld body, simultaneously or separately, an RF signal having the first frequency and a microwave signal having the second frequency; wherein the inner conductor is electrically connected to the or each first conductive element and the outer conductor is electrically connected to the or each second conductive element to enable one or both opposed surfaces (208, 210) of the instrument tip to emit independently the RF signal and the microwave signal, and wherein the first and second conductive elements are arranged at the opposed surface of the respective clamping member to act: as active and return electrodes to transfer RF EM energy into biological tissue by conduction from the respective clamping member, and as an antenna to radiate microwave EM energy into biological tissue from the opposed surface of the respective clamping member. as active and return electrodes to transfer RF EM energy into biological tissue by conduction from the respective clamping member, and as an antenna to radiate microwave EM energy into biological tissue from the opposed surface of the respective clamping member.