An exemplary implantable prosthetic device has a coaption element and at least one anchor. The coaption element is configured to be positioned within the native heart valve orifice to help fill a space where the native valve is regurgitant and form a more effective seal. The coaption element can have a structure that is impervious to blood and that allows the native leaflets to close around the coaption element during ventricular systole to block blood from flowing from the left or right ventricle back into the left or right atrium, respectively. The coaption element can be connected to leaflets of the native valve by the anchor.