High resistivity measurements are particularly sensitive to the extraneous background currents that plague any low current measurement. The Alternating Polarity method outlined in this white paper makes it possible to measure high resistivities with precision without the delays necessary for background currents to decay to a sufficiently low level. This method allows the measurement of extremely high resistivities with a repeatability of a few percent, even in the presence of background currents that would otherwise lead to literally infinite error.