We study the transport through a shunted surface superlattice system in the presence of an external magnetic field. Such a system consists of a weakly doped, instability free superlattice (shunt) that is overgrown on the edge with a two-dimensional electron system (surface superlattice). A magnetic field parallel to a static applied electric field along the superlattice axis induces current resonances in the shunt characteristics which are explained by Stark-cyclotron resonances. These resonances support the conclusion that the field alignment in the shunted surface superlattice structure is homogeneous. An increasing magnetic field perpendicular to the transport direction leads to characteristic crossings of the current-voltage characteristics of both shunt and surface superlattice. They are explained by a semiclassical model which assumes a competition between the magnetic and electric localization of the miniband electrons. We conclude that our structure indeed presents a domain free high density superlattice and might therefore be a promising candidate for the realization of an active electrically driven Bloch oscillator.