We present an analytical approach to the calculation of the linewidth and lineshift of an atom or molecule in the near field of a structured dielectric surface. For soft surface corrugations with amplitude lambda/50, we find variations of the linewidth in the ten percent region. More strikingly, the shift of the molecular resonance can reach several natural linewidths. We demonstrate that the lateral resolution is of the order of the molecule-surface distance. We give a semiquantitative explanation of the outcome of our calculations that is based on simple intuitive models.