Nonuniform current distribution at an electrode surface can complicate the measurement of ohmic and polarization resistances. The problem is investigated theoretically for a rectangular cell with electrodes of different sizes placed symmetrically at the opposite surfaces of the electrolyte, a situation typical for solid-state electrochemical cells. Solutions obtained for the secondary distribution problem show that the error in the measured polarization resistance may become large if the electrode reaction is fast, or the electrolyte conductivity low. Moreover, kinetic limitations at the counter electrode may cause distortion of the measured overpotential in cells with thin electrolytes, leading to significant errors in the measured polarization resistance. The overpotentials at the two electrodes become experimentally indistinguishable under such conditions. The geometrical and electrochemical conditions which cause such errors are becoming increasingly realistic for the state-of-the-art components under development for solid oxide fuel cells, characterized by thin electrolyte layers and improved reaction rates at the cathode. The use of thick electrolytes and/or working electrodes which are much smaller than the counter electrode may alleviate the problem related to the polarization of the counter electrode. Correction of the measured data by use of theoretical models is another possibility.