Electromagnetic induction in three two-dimensional models of conductors with two regions of different conductivity is considered. Solutions are obtained for both the H-polarization and E-polarization cases by a numerical method. Apparent resistivity as a function of period is plotted for various locations relative to the surface contact. For the H-polarization case, the apparent resistivity values calculated for points near the surface contact are affected by the varying surface charge on the interface between the regions, and a value different from the expected value is obtained. In the E-polarization case the apparent resistivity curves exhibit a "dip" characteristic when the apparent resistivity is calculated for surface points near a shelf or step structure. In both cases the value of apparent resistivity calculated at or near surface contacts between different conducting regions depends greatly on the sub-surface structure.