Methods, delivery systems and engaging apparatuses for the placement and treatment of an insufficient or stenotic cardiac valve, such as the mitral valve are disclosed. One such method is based on a two step procedure, where during the first step the engaging apparatus is brought to the valve annulus using a delivery system which permits continued normal blood flow. In some preferred embodiments, this is implemented with a balloon and other preferred embodiments it is implemented using a multi-pronged structure that is collapsible like an umbrella frame. The second step is performed after the engaging apparatus has been integrated into the annular wall by natural processes of tissue healing and remodeling. In the second step the engaging apparatus is tightened leading to tightening of the valve annulus and correction of existing valvular insufficiency. Optionally, an artificial valve may be anchored to the engaging apparatus during the same or subsequent procedure to correct either valvular insufficiency or stenosis.
