The paper presents a posteriori error estimation strategy in the parametric integral equation system (PIES). It uses collocation point differences between solutions obtained numerically by PIES and another solutions interpolated based on the initial PIES analysis. Various techniques for interpolation are proposed: by repeating the interpolation omitting one collocation point, by interpolating using only values from adjacent collocation points and by the one degree higher polynomial obtained using the least squares approximation. This allows the calculation of local and global percentage error using the integral over the mentioned differences. Finally, it can be applied to ensure convergence of the solutions using the PIES method or to adaptive refinement of distribution or number of collocation points by identifying boundary regions where the error is relatively high.