Interest in small molecules that target RNA is flourishing, and the expectation set on them to treat diseases with unmet medical needs is high. However, several challenges remain, including difficulties in selecting suitable tools and establishing workflows for their discovery. In this context, we optimized experimental and computational approaches that were previously employed for the protein targets. Here, we demonstrate that a fluorescence-based assay can be effectively used to screen small molecule libraries for their ability to bind and stabilize an RNA stem-loop. Our screen identified several fluoroquinolones that bind to the target stem-loop. We further probed their interactions with the target using biolayer interferometry, isothermal titration calorimetry (ITC), and nuclear magnetic resonance spectroscopy. The results of these biophysical assays suggest that the fluoroquinolones bind the target in a similar manner. Armed with this knowledge, we built models for the complexes of the fluoroquinolones and the RNA target. Then, we performed fragment molecular orbital (FMO) calculations to dissect the interactions between the fluoroquinolones and the RNA. We found that the binding free energies obtained from the ITC experiments correlated strongly with the interaction energies calculated by FMO. Finally, we designed fluoroquinolone analogues and performed FMO calculations to predict their binding free energies. Taken together, the results of this study support the importance of conducting orthogonal assays in binding confirmation and compound selection and demonstrate the usefulness of FMO calculations in the rational design of RNA-targeted small molecules.