Scanning acoustic microscopy (SAM) is a well-accepted imaging modality for forming quantitative, two-dimensional maps of acoustic properties of soft tissues at microscopic scales. The quantitative maps formed using our custom SAM system using a 250-MHz single-element transducer have a nominal resolution of 7 μm, which is insufficient for some investigations. To enhance spatial resolution, a SAM system operating at even higher frequencies could be designed, but associated costs and experimental difficulties are challenging. Therefore, the objective of this study is to evaluate the potential of super-resolution (SR) image processing to enhance the spatial resolution of quantitative maps in SAM. To the best of our knowledge, this is the first attempt at using post-processing, image-enhancement techniques in SAM. Results of realistic simulations and experimental data acquired from a standard resolution test pattern confirm the improved spatial resolution and the potential value of using SR in SAM.