A sewing ring for prosthetic heart valves that is connected and configured to pivot outward. A biocompatible fabric covering surrounds at least a portion of the sewing ring, and the ring may be exclusively connected to a stent with the fabric. The sewing ring may be generally planar and of uniform thickness, or may be of varying thickness. The fabric may be used to encompass both the stent and the sewing ring, and may be a single piece. A seam may be provided in the fabric as a discrete pivoting line. The sewing ring may be convertible between bi-stable positions. The ring may extend outward in a frusto-conical shape so as to enable inversion between a position facing the inflow end of the valve and a position facing the outflow end of the valve. The sewing ring may have a compliant insert having a celled construction defined by outer walls and inner ribs. A method of implantation, and a method of assembly of the heart valve is also provided.