Despite the prospect of next-generation electronic technologies spurring the investigation of the remarkable topological magnetoelectric response, its potential remains largely unexplored in the application of basic electronic devices. In this paper, we undertake this task at the theoretical level by addressing the electrodynamics and examine electromagnetic properties (e.g., tunable inductance, operating frequency range, and power consumption) of three fundamental passive magnetic devices endowed with this effect: the primitive transformer, the bilayer solenoid inductor, and the solenoid actuator. We further exploit the methodology of magnetic circuits to obtain an extended Hopkinson’s law that is valid for both topological and ordinary magnetoelectric responses (provided it is uniform in the bulk). Under low-power conditions, we find out that the functionally passive part of the topological-magnetoelectric transformer, the solenoid inductor as well as the solenoid actuator, is indistinguishable from the conventional situation up to second order in the magnetoelectric susceptibility; we argue that the main benefit of using topological insulators essentially relies on a lower power consumption. Our theoretical framework is also convenient to analyze magnetoelectric inductors endowed with a relatively large magnetoelectric susceptibility, they display a broad inductance tunability of over 200% up to 100 GHz in the millimeter length scale. Conversely, our treatment predicts that the operating frequency range could be restricted below the ultralow frequency by a significantly strong magnetoelectric response (e.g., retrieved by certain multiferroic heterostructures).