A prosthetic valve assembly for use in replacing a deficient native valve comprises a replacement valve supported on an expandable prosthesis frame. The valve may be delivered transluminally or transmyocardially using a thorascopic or other limited access approach using a delivery catheter. Preferably, the initial partial expansion of the valve is performed against the native valve annulus to provide adequate anchoring and positioning of the valve as the remaining portions of the valve expand. The valve may be delivered using a retrograde or antegrade approach. When delivered using a retrograde approach, a delivery catheter with a pull-back sheath may be used, while antegrade delivery is preferably performed with a delivery catheter with a push-forward sheath that releases the proximal end of the valve first.