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An important aspect to understanding near-field optics and imaging involves the electromagnetic scattering characteristics of objects illuminated by the near field of a sub-wavelength-sized aperture. This paper addresses one particular application of near-field optics: a transmission-mode near-field scanning microscope (NSM). Specifically, some peculiar phenomena are investigated including a near-field focusing effect, as well as an impedance-based image-shape effect. To this end, we first describe the physical attributes of an NSM and then present two computational models we use to characterize this instrument. Both moment-method and finite-difference time-domain models are discussed. These two models are applied to the analysis of the NSM for various configurations and compared to other theoretical and experimental results. Finally, the construction of an X-band NSM is described - which we label a near-field scanning microwave microscope (NSMM) - and the experimental near-field imaging measurements are compared with our numerical predictions.