Charge transport in AgI subject to an external magnetic field is studied via computer simulations. We demonstrate that a recently developed algorithm can effectively complement problematic experiments to detect the ionic Hall effect, and identify previously unreported effects such as ionic magnetoresistance. We focus first on the charge transport properties of superionic AgI, showing that the magnetic field induces a considerable reduction in the diagonal elements of the conductivity tensor (magnetoresistance). Within the limits of the signal-to-noise ratio, calculation of the off-diagonal elements of this tensor also shows the onset of the Hall effect in this material. We then present numerical evidence supporting the use of the Nerst-Einstein approximation to obtain the Hall mobility of the system. This approximation enables very efficient detection of the Hall signal, with values of the mobility and of the migration activation energy in very good agreement with experiments. Having validated our simulation approach, we consider melted AgI to investigate if the Hall signal persists in this nonsuperionic case, finding a detectable signal. Comparison of the diffusion tensor of this system with that of molten NaCl also indicates why the Hall signal is absent in the latter. This work paves the way for the routine use of simulations to study transport, and in particular the ionic Hall effect, in ionic systems under external magnetic field.