The instrument comprises a proximal coaxial transmission line for conveying microwave electromagnetic (EM) energy, a distal radiating portion and an intermediate impedance transformer 204 arranged to match an impedance of the coaxial transmission line to an impedance of the distal radiating portion. The distal radiating portion 206 comprises a microwave antenna 218 for emitting the microwave EM energy conveyed by the coaxial transmission line. The distal radiating portion has a maximum outer diameter less than an outer diameter of the coaxial transmission line 202. With these features, the instrument is able to deliver microwave energy via a small diameter structure and is suitable for insertion into a pancreas via a surgical scoping device such as an ultrasound-enabled endoscope, to provide a rapid and accurate alternative to known RF ablation techniques.