A method for simulating electronic transport through molecular junctions subjected to time-dependent external magnetic fields is developed. The method constitutes a merge of the magnetic extended Hückel Theory and the driven Liouville von Neumann approach. The former accounts for orbital magnetic effects in molecular systems whereas the latter enables simulating electron dynamics in open quantum systems within single-particle treatments. The method is demonstrated on simplistic model systems of Aharonov-Bohm molecular interferometers consisting of hydrogen rings connected to two hydrogen chain leads. Depending on the angular separation between the leads and the value of the magnetic flux, the current flowing through the system can be switched-on or -off by the application of the external field. For the system parameters considered herein the response time of the system is ~15 fs. During this period the system exhibits oscillatory transient currents prior to reaching the new steady-state. Visualizing the electron density variations in the transient period reveals how dynamic interference effects modify the transport paths through the system. These results demonstrate the capabilities of the developed methodology to study fundamental transport mechanisms of complex molecular junctions subjected to time-dependent external magnetic fields. This, in turn, may lead to the rational design of molecular switches with controllable operational frequencies.