With increasingly-violent, extreme weather events, floods are an especially daunting threat. Our proactive attempts at managing flood hazards are constantly evolving and, as of late, reinforced by advances in machine learning and remote sensing techniques. Flood Inundation Maps (FIMs) provide valuable information for developing effective, pre-flood mitigation strategies for large regions of interest, provided they are of sufficiently high spatial resolution. To this end, leveraging existing remote sensing products only yields low-resolution FIMs. Alternatively, numerically obtaining FIMs of sufficiently high spatial resolution via physics-based modeling remains a computationally-intensive process. This pilot work explores the viability of downscaling (upsampling) low-resolution FIMs to an appropriate spatial resolution via a deep super-resolution technique. Specifically, we utilize a multi-layer Residual Deep Network (RDN) to gradually downscale (300m to 30m resolution) FIMs derived for the state of Iowa, as a proof of concept. To enhance the accuracy of the resulting FIMs, we incorporate relevant Digital Elevation Maps (DEMs) data at a resolution of 30m. In this manner, our approach considers topographical features such as the horizontal and vertical reach to the nearest drainage, which are easily extracted from DEMs. We further investigate the degree to which such topographic features enhance such super-resolution tasks. Finally, our approach offers two main advantages. First, once our RDN is trained, generating high-resolution FIMs via downscaling can be orders of magnitude faster than physics-based modeling approaches. Secondly, judging from our preliminary results, opportunities arise to utilize widely-available remote sensing products to produce high-resolution FIMs, potentially rendering our approach applicable on a global scale.