A prosthetic device for sealing a native heart valves to prevent or reduce regurgitation comprises a spacer having one or more anchors. The spacer may also have atrial support structures, ventricular support structures, or both atrial and ventricular support structures In some cases, the spacer has anchors that attach to the leaflets as well as atrial and ventricular support. In some cases, the spacer straddles the annulus and is located by anchors, and in some cases the support structures can be implanted within the native heart valve. In some cases, the prosthetic device reduces the annulus diameter when implanted within the native heart vasculature. In some cases, the prosthetic device cinches the annulus when implanted within the native heart vasculature.