RNA molecules are key players in numerous cellular processes and are characterized by a complex relationship between structure, dynamics, and function. Despite their apparent simplicity, RNA oligonucleotides are very flexible molecules, and understanding their internal dynamics is particularly challenging using experimental data alone. We show how to reconstruct the conformational ensemble of four RNA tetranucleotides by combining atomistic molecular dynamics simulations with nuclear magnetic resonance spectroscopy data. The goal is achieved by reweighting simulations using a maximum entropy/Bayesian approach. In this way, we overcome problems of current simulation methods, as well as in interpreting ensemble- and time-averaged experimental data. We determine the populations of different conformational states by considering several nuclear magnetic resonance parameters and point toward properties that are not captured by state-of-the-art molecular force fields. Although our approach is applied on a set of model systems, it is fully general and may be used to study the conformational dynamics of flexible biomolecules and to detect inaccuracies in molecular dynamics force fields.