Hydrodynamic interactions play an important role in the transport of analytes through nanoscale devices. Of particular note is the role that no-slip boundary conditions have on the drag coefficient of confined particles and molecules. In this work, we use a coarse grained molecular dynamics model to measure the diffusion coefficients of proteins confined within cylindrical nanochannels of similar dimension. Finite-size corrected bulk diffusion coefficients are found to agree with experimental data, while in channels, a good match is found between theoretical expressions based on continuum fluid mechanics and the reduction of the translational diffusion coefficient across a range of protein to channel size ratios. These results demonstrate that it is possible to directly use molecular simulation to make quantitative predictions of the effects of hydrodynamics on diffusion at length scales of order 1 nm.