Disclosed are appendage mountable electronic systems and related methods for covering and conforming to an appendage surface. A flexible or stretchable substrate has an inner surface for receiving an appendage, including an appendage having a curved surface, and an opposed outer surface that is accessible to external surfaces. A stretchable or flexible electronic device is supported by the substrate inner and/or outer surface, depending on the application of interest. The electronic device in combination with the substrate provides a net bending stiffness to facilitate conformal contact between the inner surface and a surface of the appendage provided within the enclosure. In an aspect, the system is capable of surface flipping without adversely impacting electronic device functionality, such as electronic devices comprising arrays of sensors, actuators, or both sensors and actuators.