Devices and methods for implantation at a native mitral valve. One embodiment of the device includes a valve support having a first region and a second region, and anchoring member having a longitudinal dimension with a first portion configured to contact tissue at the non-circular annulus, a second portion configured to be attached to the valve support, and a lateral portion transverse to the longitudinal dimension between the first portion and the second portion. The anchoring member and the valve support are configured to move from a low-profile configuration to an expanded configuration in which the first portion of the anchoring member at least partially adapts to the non-circular annulus of the native mitral valve and a shape of the first region of the valve support is at least partially independent of a shape of the first portion of the anchoring member.
