Topographic maps are commonly constructed from electrical scalp recordings (suchas EEGs and ERPs) using several different interpolation methods. It is importantto determine the accuracy of such maps. Previous assessments of interpolation methods have been based on global error measures and the visual appearance of the topographic maps. However, the relationship of interpolation error to local contributing factors requires a more detailed analysis. In this paper, we use simulations to explore and quantify the relationship of error to global and local factors for different interpolation methods. We find that among the best interpolation methods, adequate electrode density is more important than the method used. For shallow sources, we show that local interpolation error is mostcorrelated with potential gradient, and has a lesser correlation with distance to nearest electrode. The greatest correlation, however, is with the product of gradient and distance. Thus, interpolation error can be controlled locally by making the interelectrode distance inversely proportional to the expected potential gradient. With shallow sources, areas far from any electrode and having high apparent gradient are likely to have high interpolation error. Moreover, all areas far from any electrode may contain high interpolation errors, and should be interpreted with caution.