Scanning capacitance microscopes can be used to imaging the topography of conducting surfaces, both free and covered by an insulating film, and also the local properties of the films. Such local properties may be the variations of the dielectric constant and/or the dielectric losses, caused by the presence of certain defects. It is usually assumed that the resolution is tip radius limited. However, below an optimum radius of a few tens of nanometers, approximately twice the tip/surface distance, the resolution does not improve, only the signal-to-noise ratio is reduced. In the case of thick dielectric films limiting becomes the thickness, In spite of that appreciable local resolution may be achieved in the surface layer of the film on the side of the probe, although at reduced contrast, While close to the probe axis the contribution of the surface layer is dominating, st larger distances sensitivity reversal may occur.