Current magnetic systems for microrobotic navigation consist of assemblies of electromagnets, which allow for the wireless accurate steering and propulsion of sub-millimetric bodies. However, large numbers of windings and/or high currents are needed in order to generate suitable magnetic fields and gradients. This means that magnetic navigation systems are typically cumbersome and require a lot of power, thus limiting their application fields. In this paper, we propose a novel propulsion method that is able to dramatically reduce the power demand of such systems. This propulsion method was conceived for navigation systems that achieve propulsion by pulling microrobots with magnetic gradients. We compare this power-efficient propulsion method with the traditional pulling propulsion, in the case of a microrobot swimming in a micro-structured confined liquid environment. Results show that both methods are equivalent in terms of accuracy and the velocity of the motion of the microrobots, while the new approach requires only one ninth of the power needed to generate the magnetic gradients. Substantial equivalence is demonstrated also in terms of the manoeuvrability of user-controlled microrobots along a complex path.