An apparatus for at least partially supporting a leaflet of a regurgitant heart valve, the apparatus comprising at least one subvalvular device defining a longitudinal axis and including: a subvalvular supporting portion including a leaflet-contacting upper supporter surface longitudinally spaced from an oppositely facing lower supporter surface, a supporter perimeter wall extending longitudinally between, and integrally and contiguously formed with both of, the upper and lower supporter surfaces (210,212), at least a portion of the supporter perimeter wall configured to contact a subvalvular cardiac wall adjacent to the heart valve, wherein the subvalvular supporting portion is at least partially formed from at least one of braided mesh strands of a first configuration, braided mesh strands of a second configuration, a balloon, and a plurality of longitudinally extending struts; an anchor portion adjacent to, and longitudinally spaced from, the upper supporter surface, the anchor portion including a leaflet-contacting lower anchor surface longitudinally spaced from an oppositely facing upper anchor surface and an anchor perimeter wall extending longitudinally between the upper and lower anchor surfaces (216,218), wherein the anchor portion is at least partially formed from at least one of braided mesh strands of a first configuration, braided mesh strands of a second configuration, a balloon, and a plurality of longitudinally extending struts; and a connector neck interposed longitudinally between, and attached to both of, the upper supporter surface and the lower anchor surface, the connector neck configured to penetrate longitudinally through at least one of a base of the leaflet and an annulus of the heart valve at a manufactured puncture site, wherein at least one of the subvalvular supporting portion and the anchor portion includes a lining substantially conforming to at least a portion of an interior surface thereof, the lining being at least partially formed from a flexible polymer material, an autograft tissue, an allograft tissue, a sheet of flexible material, braided mesh strands of the first configuration, braided mesh strands of the second configuration, a balloon, a plurality of longitudinally extending struts, or any combination thereof, wherein the subvalvular supporting portion includes a separately provided covering material the covering material is connected to the apparatus at the connector neck and selectively contacts an outer surface of the subvalvular supporting portion, wherein at least a portion of the covering material is spaced apart from at least a portion of the outer surface of the subvalvular supporting portion, with an intervening volume therebetween during at least a portion of a use cycle of the apparatus. a subvalvular supporting portion including a leaflet-contacting upper supporter surface longitudinally spaced from an oppositely facing lower supporter surface, a supporter perimeter wall extending longitudinally between, and integrally and contiguously formed with both of, the upper and lower supporter surfaces (210,212), at least a portion of the supporter perimeter wall configured to contact a subvalvular cardiac wall adjacent to the heart valve, wherein the subvalvular supporting portion is at least partially formed from at least one of braided mesh strands of a first configuration, braided mesh strands of a second configuration, a balloon, and a plurality of longitudinally extending struts; an anchor portion adjacent to, and longitudinally spaced from, the upper supporter surface, the anchor portion including a leaflet-contacting lower anchor surface longitudinally spaced from an oppositely facing upper anchor surface and an anchor perimeter wall extending longitudinally between the upper and lower anchor surfaces (216,218), wherein the anchor portion is at least partially formed from at least one of braided mesh strands of a first configuration, braided mesh strands of a second configuration, a balloon, and a plurality of longitudinally extending struts; and a connector neck interposed longitudinally between, and attached to both of, the upper supporter surface and the lower anchor surface, the connector neck configured to penetrate longitudinally through at least one of a base of the leaflet and an annulus of the heart valve at a manufactured puncture site, wherein at least one of the subvalvular supporting portion and the anchor portion includes a lining substantially conforming to at least a portion of an interior surface thereof, the lining being at least partially formed from a flexible polymer material, an autograft tissue, an allograft tissue, a sheet of flexible material, braided mesh strands of the first configuration, braided mesh strands of the second configuration, a balloon, a plurality of longitudinally extending struts, or any combination thereof, wherein the subvalvular supporting portion includes a separately provided covering material the covering material is connected to the apparatus at the connector neck and selectively contacts an outer surface of the subvalvular supporting portion, wherein at least a portion of the covering material is spaced apart from at least a portion of the outer surface of the subvalvular supporting portion, with an intervening volume therebetween during at least a portion of a use cycle of the apparatus.