A method and apparatus for functionally occluding the lumen of the left atrial appendage (LAA) is provided. Access to the LAA is through an epicardial approach. The devices function to capture the LAA through various non-invasive means. After capturing the LAA with the devices and methods provided, a clamping device is preferably disposed about the base of the appendage. In certain embodiments, the appendage remains viable subsequent to the functional occlusion of the lumen.