We present a systematic analysis of the effects that the microscopic parts of electrostatic force microscopy probes ( the cone and cantilever) have on the electrostatic interaction between the tip apex and thick insulating substrates ( thickness > 100 mu m). We discuss how these effects can influence the measurement and quantification of the local dielectric constant of the substrates. We propose and experimentally validate a general methodology that takes into account the influence of the cone and the cantilever, thus enabling us to obtain very accurate values of the dielectric constants of thick insulators.