Several theoretical forms of the dependence of the electrode differential capacitance on the electrode potential (capacitance curves) have been examined in the context of their effectiveness in fitting experimental data. Each curve has been derived from a rigorously defined physical model. The link between the capacitance curve and the model has been clearly indicated. The goodness of fit and the curvature measures of non-linearity (maximum intrinsic and maximum parameter effects non-linearity, defined in the paper) served as a criterion for the acceptance or rejection of a particular curve and the related model. A new computer program that facilitates the fitting is briefly described. This user-interactive program enables non-linear fitting of an arbitrary capacitance curve, provides fitted data, together with residuals and the dependence of surface coverage on the electrode potential, and calculates the standard deviations for the parameter estimates, their Student t values and the matrix of parameter correlation coefficients, Additionally, the program provides Box’s bias of the parameters and both maximum intrinsic and maximum parameter effects curvature measures. If required, the program output can be arranged to deliver simultaneously the dependence of surface charge density on electrode potential or surface coverage, the theoretical electrocapillary curves and other related information. The two-dimensional grids of the non-linear least-squares solution locus for some parameters are presented. The quality of fit is demonstrated for a few examples. The two-, three- and four-parameter models considered in this paper were unable to fit the experimental data within accepted experimental errors although they did not show any other extraordinary deficiencies. No definite conclusions were reached regarding the six-parameter models considered. Some of them can fit the data within experimental error but more work is required on reparametrization. Some six-parameter models behaved equally well from statistical point of view.