Since potential changes in the dynamics and mobility of drugs upon complexation for delivery may affect their ultimate efficacy, we have investigated the dynamics of two local anesthetic molecules, bupivacaine (BVC, C18H28N2O) and ropivacaine (RVC, C17H26N2O), in both their crystalline forms and complexed with water-soluble oligosaccharide 2-hydroxypropyl-β-cyclodextrin (HP-β-CD). The study was carried out by neutron scattering spectroscopy, along with thermal analysis, and density functional theory computation. Mean square displacements suggest that RVC may be less flexible in crystalline form than BVC, but both molecules exhibit very similar dynamics when confined in HP-β-CD. The use of vibrational analysis by density functional theory (DFT) made possible the identification of molecular modes that are most affected in both molecules by insertion into HP-β-CD, namely those of the piperidine rings and methyl groups. Nonetheless, the somewhat greater structure in the vibrational spectrum at room temperature of complexed RVC than that of BVC, suggests that the effects of complexation are more severe for the latter. This unique approach to the molecular level study of encapsulated drugs should lead to deeper understanding of their mobility and the respective release dynamics.