Measurements of the Ag+ transference numbers in 0.1025 and 1.010 M aqueous silver nitrate solutions were used to verify the accuracy of the galvanostatic polarization method for transference number determinations in concentrated solutions of binary electrolytes. Simulations were performed to analyze the experimental data and sources of error. Experimental results were within 4% of literature values at 0.1025 M and within 9% at 1.010 M, the latter presumably due to a deviation from the method's assumption of a convection-free system. The method should be immune to convection when used in polymer electrolytes (for which it was originally developed) and is expected to be accurate to 4% or better in such systems. Three improvements, i.e., a new extrapolation method, a refined fitting procedure, and a means of identifying problematic runs have also been incorporated into the galvanostatic polarization method and are described.