Despite the widespread use of cyclization as a structure optimization tool in peptide chemistry, little is known about the effect of cyclization on peptide internal dynamics. Here we used a combination of multi-field NMR relaxation and molecular dynamics techniques to study monocyclic as well as polycyclic peptides that have promising biopharmaceutical properties - VH, SFTI-1 and cVc1.1 - and their less constrained analogues to study the effect of backbone cyclization (which forms a macrocycle) and disulfide bond cyclization (which forms internal cycles). We confirmed that backbone cyclization contributes to the rigidity of the monocyclic VH. Interestingly though, backbone cyclization of the bicyclic SFTI-1 had a limited effect on rigidity, with changes in internal dynamics localized around the ligation site. This suggests that the disulfide bond, which creates an internal cycle, has a insulating effect, protecting the internal cycle from external motional effects. An insulating effect was also observed for the polycyclic cVc1.1 - the rigidity of the core was not enhanced by macrocyclization. Additionally, we found that disulfide bonds had a greater contribution to overall rigidity than macrocyclization. Overall, our results suggest that, although backbone cyclization can improve rigidity, there is a complex interplay between dynamics and cyclization, particularly for polycyclic systems.