A strap-on mounting apparatus includes a chassis having a frame formed by a pair of spaced-apart brackets having flexible couplings for removably mounting the mounting apparatus on a wearer's arm or leg extremity. The chassis rotatably supports a cradle that is structured for removably mounting a hand-held portable device of a type normally carried by people on their person. The cradle is rotatable relative to the chassis between different relative orientations. For example, the cradle is rotatable relative between a normal operational orientation that is substantially cross-wise to the arm or leg extremity, and a normal stored orientation that is substantially aligned with the extremity, with the cradle passing through a continuous series of intervening rotational orientations any of which may be useful as an operational orientation.