In the present work, we developed a computational framework to calculate cross-correlated relaxation rates for methyl groups in protein side chains from all-atom MD simulations. The relaxation rates are computed by determining the cross-TCFs and fitting them with a 2-or 4parameter analytical model (LS2 or 4P, respectively). Using the protein ubiquitin as a model system, it is found that the CCR rates are insensitive to the fitting model used and that the 4P model does not lead to more accurate relaxation rates. MD simulations with the AMBER ff99SB*-ILDN and CHARMM36 protein force fields in combination with the TIP4P/2005 water model yield overall protein tumbling times that are in close agreement with experiment.