NMR microscopy is routinely employed in fields of science such as biology, botany, and materials science to observe magnetic parameters and transport phenomena in small scale structures. Despite extensive efforts, the resolution of this method is limited (>10 microm for short acquisition times), and thus cannot answer many key questions in these fields. We show, through theoretical prediction and initial experiments, that ESR microscopy, although much less developed, can improve upon the resolution limits of NMR, and successfully undertake the 1 mum resolution challenge. Our theoretical predictions demonstrate that existing ESR technology, along with advanced imaging probe design (resonator and gradient coils), using solutions of narrow linewidth radicals (the trityl family), should yield 64 x 64 pixels 2D images (with z slice selection) with a resolution of 1 x 1 x 10 microm at approximately 60 GHz in less than 1h of acquisition. Our initial imaging results, conducted by CW ESR at X-band, support these theoretical predictions and already improve upon the previously reported state-of-the-art for 2D ESR image resolution achieving approximately 10 x 10 mum, in just several minutes of acquisition time. We analyze how future progress, which includes improved resonators, increased frequency of measurement, and advanced pulsed techniques, should achieve the goal of micron resolution.