An approach is presented to directly simulate the dynamics of methyl groups in protein side-chains, as accessible via NMR spin relaxation measurements, by all-atom MD simulations. The method, which does not rely on NMR information or any system-specific adjustable parameters, is based on calculating the time-correlation functions (TCFs) of the C-H bonds in methyl groups and explicitly takes the truncation of the TCFs due to overall tumbling of the molecule into account. Using ubiquitin as a model protein, we show (i) that an accurate description of the methyl dynamics requires reparametrization of the potential energy barriers of methyl group rotation in the AMBER ff99SB*-ILDN force field (and related parameter sets), which was done with CCSD(T) coupled cluster calculations of frequency isolated dipeptides as reference, and (ii) that the TIP4P/2005 solvation model yields overall tumbling correlation times that are in close agreement with experimental data. The methyl axis squared order parameters S-axis(2) and associated correlation times tau(f), obtained within the Lipari-Szabo formalism, are in good agreement with the values derived from NMR deuterium relaxation experiments. Importantly, the relaxation rates and spectral densities derived from MD and NMR agree as well, enabling a direct comparison without assumptions inherent to simplified motional models.