A valve prosthesis (43), such as an artificial venous valve, having a support frame (11) and leaf structure comprising one or more leaflets (78, 79) in which the outer edge (112) of each leaflet engages the inner circumference of the bodily passageway along a serpentine path urged against the passageway by an expandable frame, while the inner edges move in response to fluid to restrict retrograde flow. Optionally, one or more elements (31, 32) can extend from the support frame/leaf structure to provide centering support and/or protection from the leaflet adhering to the vessel wall. In one embodiment, the centering support structure (164) comprises a second or third expandable frames (31, 32) attached to and extending from the proximal and/or distal ends of main valve structure and support frame. In another embodiment, one or more support elements extend outward from the valve support frame to engage the vessel wall to provide greater longitudinal stability.