In ceria-based catalysis, the shape of the catalyst particle, which determines the exposed crystal facets, profoundly affects its reactivity. The vibrational frequency of adsorbed carbon monoxide (CO) can be used as a sensitive probe to identify the exposed surface facets, provided reference data on well-defined single crystal surfaces together with a definitive theoretical assignment exist. We investigate the adsorption of CO on the CeO2 (110) and (111) surfaces and show that the commonly applied DFT(PBE) + U method does not provide reliable CO vibrational frequencies by comparing with state-of-the-art infrared spectroscopy experiments for monocrystalline CeO2 surfaces. Good agreement requires the hybrid DFT approach with the HSE06 functional. The failure of conventional density-functional theory (DFT) is explained in terms of its inability to accurately describe the facet- and configuration-specific donation and backdonation effects that control the changes in the C-O bond length upon CO adsorption and the CO force constant. Our findings thus provide a theoretical basis for the detailed interpretation of experiments and open up the path to characterize more complex scenarios, including oxygen vacancies and metal adatoms.