Prosthetic heart valve devices and associated methods for percutaneous heart valve replacement are disclosed herein. A transcatheter valve prosthesis configured in accordance herewith includes a frame having a valve support and one or more support arms coupled thereto. The one or more support arms are configured to extend from the second end of the valve support toward the first end when the valve prosthesis is in an expanded configuration. When deployed in the expanded configuration, the one or more support arms have a curvilinear shape, such as a substantially S-shape, that at least partially engages tissue at the native heart valve.
