The quest for swimming microrobots originates from possible applications in medicine, especially involving navigation in bodily fluids. Swimming microorganisms have become a source of inspiration because their propulsion mechanisms are effective in the low-Reynolds number regime. In this study, we address a propulsion mechanism inspired by metachronal waves, i.e. the spontaneous coordination of cilia leading to the fast swimming of ciliates. We analyse the biological mechanism (referring to its particular embodiment in Paramecium caudatum), and we investigate the contribution of its main features to the swimming performance, through a three-dimensional finite-elements model, in order to develop a simplified, yet effective artificial design. We propose a bioinspired propulsion mechanism for a swimming microrobot based on a continuous cylindrical electroactive surface exhibiting perpendicular wave deformations travelling longitudinally along its main axis. The simplified propulsion mechanism is conceived specifically for microrobots that embed a micro-actuation system capable of executing the bioinspired propulsion (self-propelled microrobots). Among the available electroactive polymers, we select polypyrrole as the possible actuation material and we assess it for this particular embodiment. The results are used to appoint target performance specifications for the development of improved or new electroactive materials to attain metachronal-waves-like propulsion.