In some embodiments, a valve prosthesis includes an inlet portion that is substantially s-shaped and configured to engage the floor of the outflow tract of the native heart atrium. In some embodiments, a valve prosthesis includes a chordae guiding element configured to reduce bending of the chordae to reduce stress on the chordae during the cardiac cycle. In some embodiments, a valve prosthesis includes a central portion having an hourglass shape configured to pinch a native annulus in order to provide axial fixation of the valve prosthesis within a valve site. In some embodiments, a valve prosthesis includes a frame having an outflow end that is flared to provide a gap between an outflow end of the frame and an outflow end of prosthetic leaflets when the prosthetic leaflets are fully opened.