MD trajectories can be viewed as "ultimate models" of disordered proteins. However, these models are in need of careful experimental validation. The coefficient of translational diffusion Dtr, measurable by pulsed-field gradient NMR, offers a measure of compactness for disordered proteins (especially useful for smaller proteins, where SAXS data are unavailable). Here we investigate, both experimentally and via MD modeling, the translational diffusion of 25-residue N-terminal fragment from histone H4 (N-H4). Prediction of Dtr requires two modifications to the standard MD modeling scheme. First, it cannot be accomplished using the standard NPT setup with Langevin thermostat, but rather requires an NVE simulation or, otherwise, NPT equipped with the so-called Bussi thermostat. We have implemented this thermostat as a part of Amber 20 package. Second, the predicted Dtr values depend on the size of the simulation box. Therefore, one needs to record a series of trajectories in boxes of increasing size and then extrapolate from these results. To deal with this requirement, we first recorded a trajectory in a small-sized box and then used the snapshots from this trajectory to start many short simulations in bigger boxes. Using these tactics, we have found that MD simulations in TIP4P-Ew water overestimate Dtr of N-H4 by ca. 20%, whereas the simulations in TIP4P-D water underestimate it by ca. 30%. Apparently, both trajectories misjudge the compactness of the N-H4 conformational ensemble. In the case of folded protein, ubiquitin, the prediction errors do not exceed ca. 10%. Of additional interest, we found that MD-predicted rotational diffusion coefficient of ubiquitin also depends on the box size. The correct value is only recovered by the TIP4P-Ew simulation in a small box, while using a large box overestimates Drot by ca. 15%. Funding: SPbU grant 51142660.