We present an analysis of the measurement error caused by the stray field of scanning capacitance microscope probes of various shapes. Cylindrical islands and wells of varying radius and height or depth, in both conducting surfaces and structures containing dielectric films, were used as test features for modelling. The results show that high accuracy and good contrast of small details are contradictory requirements. Probes with small radius of curvature of the tip apex yield smaller errors on features with small diameter but larger ones on features with large diameter than tips with large radius of curvature. The stray electrostatic field causes large errors, which are exceptionally severe with microfabricated probes. Contrary to general belief, differential measurements, based on modulation of the probe/sample separation or of the width of depletion layer in semiconductors, do not reduce the effect of the stray field significantly. For best results, the probe should be shielded as close to the tip apex as possible. In the case of microfabricated probes, at least the side of the cantilever facing the sample should be shielded.