Disclosed herein are representative embodiments of methods, apparatus, and systems used to deliver a prosthetic heart valve to a deficient valve. In one embodiment, for instance, a support structure and an expandable prosthetic valve are advanced through the aortic arch of a patient using a delivery system. The support structure is delivered to a position on or adjacent to the surface of the outflow side of the aortic valve (the support structure defining a support-structure interior). The expandable prosthetic valve is delivered into the aortic valve and into the support-structure interior. The expandable prosthetic heart valve is expanded while the expandable prosthetic heart valve is in the support-structure interior and while the support structure is at the position on or adjacent to the surface of the outflow side of the aortic valve, thereby causing one or more native leaflets of the aortic valve to be frictionally secured between the support structure and the expanded prosthetic heart valve.