We have used the finite element method to study the extraordinary magnetoresistance (EMR) effect of semiconductor-metal hybrid structures in rectangular device geometries. These have recently been found to exhibit intriguing properties interesting for magnetic-field sensors. Current and potential distributions in the devices are calculated in an applied magnetic field. By these means, we investigate the EMR effect, in particular, as a function of material parameters and of the contact resistance ρc between the semiconductor and the metal. In our calculations we find that ρc should be within a specific operation regime in order to obtain a pronounced magnetoresistance effect. We show that by means of the electron mobility in the semiconductor the voltage and the current sensitivity of a hybrid device can be optimized with respect to an operation field in the 10-mT range.