We present numerical calculations for a model illumination mode Scanning Near-field Optical Microscope (SNOM) that provide some guidelines for the determination of the resolution of such instruments. The calculations of the near-field intensity distribution inside the tapered waveguide show that the metal employed in their coating determines the degree of confinement of the radiation and, thus, the size of the effective source at the exit end of the waveguide. It is argued that simple measure of the ultimate resolution of near-field microscopes is provide by the skin depth of the metal employed in the coating of the tapered waveguide. These ideas are supported by the calculated near- field intensity distributions in the neighborhood of the tapered waveguide, and by the simulated images of a two-cylinder object.