A surgical instrument (100) (e.g. scalpel) is disclosed which has an antenna arranged to emit a substantially uniform microwave radiation field (e.g. having a frequency of 5-100 GHz) at an edge of a cutting element (110) (e.g. blade). The emitted radiation can cauterize tissue e.g. broken blood vessels simultaneously with cutting. The antenna may be integral with the cutting element, e.g. a metallized piece of ceramic attachable at an end of a waveguide (120, 150) to receive radiation therefrom. The cutting element (110) can include a quarter wave transformer to couple power efficiently from the waveguide (120). The instrument can be used with impedance matching apparatus to control the energy delivered into the tissue. Also disclosed is an invasive ablation probe (e.g. insertable through a catheter) having a plurality of radiating elements whose emitted field combine to give a uniform effect at an insertion end of the probe.