Quantitative acoustic microscopy (QAM) permits the formation of quantitative two-dimensional (2D) maps of acoustic and mechanical properties of soft tissues at microscopic resolution. The 2D maps formed using our custom SAM systems employing a 250-MHz and a 500-MHz single-element transducer have a nominal resolution of 7 μm and 4μm, respectively. In a previous study, the potential of single-image super-resolution (SR) image post-processing to enhance the spatial resolution of 2D SAM maps was demonstrated using a forward model accounting for blur, decimation, and noise. However, results obtained when the SR method was applied to soft tissue data were not entirely satisfactory because of the limitation of the convolution model considered and by the difficulty of estimating the system point spread function and designing the appropriate regularization term. Therefore, in this study, a machine learning approach based on convolutional neural networks was implemented. For training, data acquired on the same samples at 250 and 500 MHz were used. The resulting trained network was tested on 2D impedance maps (2DZMs) of human lymph nodes acquired from breast-cancer patients. Visual inspection of the reconstructed enhanced 2DZMs were found similar to the 2DZMs obtained at 500 MHz which were used as ground truth. In addition, the enhanced 250-MHz 2DZMs obtained from the proposed method yielded better peak signal to noise ratio and normalized mean square error than those obtained with the previous SR method. This improvement was also demonstrated by the statistical analyses. This pioneering work could significantly reduce challenges and costs associated with current very high-frequency SAM systems while providing enhanced spatial resolution.