Devices and methods for implantation at a native mitral valve having a non-circular annulus and leaflets. One embodiment of the device includes a valve support having a first region configured to be attached to a prosthetic valve with a plurality of prosthetic leaflets and a second region. The device can further include an anchoring member having a longitudinal dimension and including 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 between the first portion and the second portion. The second portion of the anchoring member is attached to the second region of the valve support while in a low-profile configuration in which the anchoring member and the valve support are configured to pass through vasculature of a human. The lateral portion is transverse to the longitudinal dimension. The anchoring member and the valve support are configured to move from the 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 the first region of the valve support is spaced inwardly from the first portion of the anchoring member relative to the longitudinal dimension of the anchoring member such that 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.