This paper compares two indirect methods of determining the maximum electrostatic potential difference across the high-latitude ionosphere. One method estimates the cross-polar-cap potential difference from solar wind parameters using a theoretical formula with empirically determined coefficients, while the other method is based on the inversion of ground magnetograms from a global network of magnetometers. These techniques are each applied to the two intervals chosen for study during the Coordinated Data Analysis Workshop (CDAW) 6. During the first interval (March 22, 1979) the potential drop predictd from solar wind parameters is in encouraging agreement with that inferred from the ground magnetograms, while for the second interval (March 31--April 1, 1979) the theoretically predicted potential drop was substantially larger than that calculated from the magnetogram inversion technique. The disagreement is likely due, in part, to uncertainties in the ionospheric conductivity model upon which the magnetogram inversion technique depends. For the March 22 interval, the conductivity model agrees reasonably well with in situ particle flux data; a similar comparison has not been made for the second interval. In addition, the March 31 interval was characterized by small-scale variations in the solar wind, which may affect the validity of the predicted value of the cross-polar-cap potential drop. The difference in the nature of the substorms within the two intervals may also be significant.