Semiconductor–metal hybrid structures can exhibit a very large geometrical magnetoresistanceeffect, the so-called extraordinary magnetoresistance (EMR) effect. Using the finite element method, we study the EMR effect in rectangular semiconductor–metal hybrid structures and investigate the effects of material parameters and of device geometry. We find that the EMR device exhibits inverse scalability, i.e., the output characteristics improve with decreasing device width. This is promising for miniaturized magnetic-field sensors like, e.g., read heads. Using realistic device parameters, we predict an optimized performance as a sensor for a width-to-length ratio of 0.025.