Anchor devices and methods used to secure a prosthetic valve to a native valve annulus are described. The anchor device can be a separate expandable element from the prosthetic valve that is first advanced to the annulus and deployed, after which an expandable prosthetic valve is advanced to within the annulus and deployed. The combination of the two elements can apply a clamping force to the valve leaflets which holds the prosthetic valve in place. The anchor device can have a lower or ventricular portion and an upper or atrial portion. The anchor device can include one or more leaflet clamping portions. One, two, or more upstanding vertical posts between the clamping portions can extend upward at the valve commissures and support the upper portion, which can include one or more structures for leak prevention.