The present invention provides a device which is adapted to press together the septum primum and the septum secundum between the atrial chambers to close any tunnel in the septum. The device in its preferred form has two clamping members, one on each side of the septum and a central connector which connects the two clamping members and passes through the tunnel. The device is configured to conform to the anatomy such that the tunnel is not substantially deformed by the device. The central connector, in its preferred form has two wires that are spaced apart so that the wires are proximate the lateral sides of the tunnel. The spacing allows the device to be centered at an appropriate location.