Cryogenic transmission electron microscopy (cryo-TEM) and super-resolution fluorescence microscopy are two popular and ever improving methods for high-resolution imaging of biological samples. In recent years, the combination of these two techniques into one correlated workflow has gained attention as a promising route towards contextualizing and enriching cryo-TEM imagery. A problem that is often encountered in the combination of these methods is that of light-induced damage to the sample during fluorescence imaging that renders the sample structure unsuitable for TEM imaging. In this paper, we describe how absorption of light by TEM sample support grids leads to sample damage, and we systematically explore the importance of parameters of grid design. We explain how, by changing the grid geometry and materials, one can increase the maximum illumination power density in fluorescence microscopy by up to an order of magnitude. Finally, we demonstrate the significant improvements in super-resolution image quality that are enabled by the selection of support grids that are optimally suited for correlated cryo-microscopy.