Spectral imaging is a ubiquitous tool in modern biochemistry. Despite acquiring dozens to thousands of spectral channels, existing technology cannot capture spectral images at the same spatial resolution as structural microscopy. Due to partial voluming and low light exposure, spectral images are often difficult to interpret and analyze. This highlights a need to upsample the low-resolution spectral image by using spatial information contained in the high-resolution image, thereby creating a fused representation with high specificity both spatially and spectrally. In this paper, we propose a framework for the fusion of co-registered structural and spectral microscopy images to create super-resolved representations of spectral images. As a first application, we super-resolve spectral images of ex-vivo retinal tissue imaged with confocal laser scanning microscopy, by using spatial information from structured illumination microscopy. Second, we super-resolve mass spectroscopic images of mouse brain tissue, by using spatial information from high-resolution histology images. We present a systematic validation of model assumptions crucial towards maintaining the original nature of spectra and the applicability of super-resolution. Goodness-of-fit for spectral predictions are evaluated through functional R2 values, and the spatial quality of the super-resolved images are evaluated using normalized mutual information.