An improved method to determine limiting currents I(L) in cation exchange membranes based on the use of a microhole array attached onto the membrane surface is applied to the Nafion(R) 117 membrane in dilute aqueous NaCl solutions. The values for I(L) obtained from the current-voltage curves are used to estimate the cation transport numbers t1s corresponding to the membrane operating under limiting current conditions. The changes of t1s with the NaCl concentration give some insights into the membrane selectivity, and cannot be described by the conventional Donnan theory for charged membranes. Instead, a two phase model accounting for different conductive phases in the membrane is able to describe the experimental trends.