The mechanisms of super-resolution imaging by contact microspherical (or microcylindrical) nanoscopy remain an enigmatic question since these lenses neither have an ability to amplify the near fields like in the case of far-field superlenses, nor they have a hyperbolic dispersion similar to hyperlenses. In this work we study theoretically and numerically the resolution of point sources which are imaged through microcylinders and microspheres. Our approach is based on a rigorous solution of the Maxwell equations for the dipole emission near dielectric microparticles. This allows us to account for various physical effects that may differentiate the regime of microsphere-based imaging from the standard microscopy. These effects include the near-field coupling to microspheres, excitation of microsphere resonances (whispering gallery modes), coherence and polarization of dipole emission. Their role in resolution will be discussed.