An implantable closure device can comprise a self-expanding metal frame comprising a central portion defining a lumen and a plurality of first anchoring arms and a plurality of second anchoring arms angularly spaced around the central portion. The central portion can comprise a sinusoidal-shaped ring defining a plurality of apices. The first anchoring arms can be connected to locations inside of the apices on a first side of the central portion and the second anchoring arms can be connected to locations inside of the apices on a second side of the central portion. The first anchoring arms can be configured to bear against a first surface of a septal wall. The second anchoring arms can be configured to bear against a second surface of the septal wall.