In recent years, the inverse pneumatic artificial muscles attained great attention in soft robotics, especially for the wider motion range compared to traditional positive pneumatic actuators. Besides self-sensing is a recognized highly desirable property for soft actuators to enable proprioception and to facilitate the soft robots control, a self-sensing strategy for a soft inverse pneumatic muscle was still missing. In this paper, we present the first self-sensing inverse pneumatic artificial muscle in which the reinforcing but compliant element that guides the actuator motion during actuation has not only a mechanical function but, being also electrically conductive, it endows the actuator with self-sensing. Here, the actuator design and manufacturing are described, together with an electromechanical characterization. In addition, we demonstrate its self-sensing capability in a dynamic setting, by predicting the actuator strain from its electric resistance variation, through a calibration model.