Devices and methods are described for ablation of cardiac tissue for treating cardiac arrhythmias, such as atrial fibrillation. Devices may include a tissue contacting member for contacting epicardial tissue and securing the ablation device to the epicardial tissue and an ablation member for ablating the tissue. Suction apertures attach the contacting member to the epicardial surface with sufficient strength to stabilize the tissue with the device. The devices and methods can be used to ablate epicardial tissue in the vicinity of a pulmonary vein or to ablate cardiac tissues in other locations on a heart. A combined pacing and ablation probe is described for treating cardiac arrhythmia by: advancing the probe through an incision into the vicinity of the patient's heart, verifying at least one location of a cardiac parasympathetic ganglion, and applying ablation energy to the cardiac parasympathetic ganglion.