The removal of the heme group from myoglobin (Mb) results in a destabilization of the protein structure. The dynamic basis of the destabilization was followed by comparative measurements on holo- (holo-Mb) and apomyoglobin (apo-Mb). Mean-squared displacements (MSD) and protein resilience on the picosecond-to-nanosecond timescale were measured by elastic incoherent neutron scattering. Differences in thermodynamic parameters, MSD, and resilience were observed for both proteins. The resilience of holo-Mb was significantly lower than that of apo-Mb, indicating entropic stabilization by a higher degree of conformational sampling in the heme-bound folded protein. Molecular dynamics simulations provided site-specific information. Averaged over the whole structure, the molecular dynamics simulations yielded similar MSD and resilience values for the two proteins. The mobility of residues around the heme group in holo-Mb showed a smaller MSD and higher resilience compared to the same residue group in apo-Mb. It is of interest that in holo-Mb, higher MSD values are observed for the residues outside the heme pocket, indicating an entropic contribution to protein stabilization by heme binding, which is in agreement with experimental results.