Devices and methods provide for ablation of cardiac tissue for treating cardiac arrhythmias such as atrial fibrillation. Although the devices and methods are often be used to ablate epicardial tissue in the vicinity of at least one pulmonary vein, various embodiments may be used to ablate other cardiac tissues in other locations on a heart. Devices generally include at least one tissue contacting member for contacting epicardial tissue and securing the ablation device to the epicardial tissue, and at least one ablation member for ablating the tissue. Various embodiments include features, such as suction apertures, which enable the device to attach to the epicardial surface with sufficient strength to allow the tissue to be stabilized via the device. For example, some embodiments may be used to stabilize a beating heart to enable a beating heart ablation procedure. Many of the devices may be introduced into a patient via minimally invasive introducer devices and the like. Although devices and methods of the invention may be used to ablate epicardial tissue to treat atrial fibrillation, they may also be used in veterinary or research contexts, to treat various heart conditions other than atrial fibrillation and/or to ablate cardiac tissue other than the epicardium. A method is described for treating cardiac arrhythmia by: verifying at least one location of a patient's cardiac parasympathetic ganglia, advancing at least one treatment member through an incision on the patient into the vicinity of the cardiac parasympathetic ganglia and applying energy to ablate at least one the cardiac parasympathetic ganglia. A combined pacing and ablation probe is described for performing the method.