A method and apparatus for transmural ablation using an instrument containing two electrodes or cryogenic probes. A clamping force is exerted on the two electrodes or probes such that the tissue of the hollow organ is clamped therebetween. Bipolar RF energy is then applied between the two electrodes, or the probes are cryogenically cooled, thus ablating the tissue therebetween. A monitoring device measures a suitable parameter, such as impedance or temperature, and indicates when the tissue between the electrodes has been fully ablated.