We have studied 1:1 inclusion complexes of two imidazole-based ionic liquids within beta-cyclodextrin: 1-dodecy1-3-methylimidazolium and 1-butyl-3-methylimidazolium. By means of an adaptive biasing force scheme, we obtained the free energy profile along two different pathways, differing in the orientations of the head-to-tail vector with respect to the primary-secondary rim axis. Regarding 1-dodecy1-3-methylimidazolium, we found one minimum energy structure for each pathway, in which the hydrophobic tail remains embedded within the cyclodextrin, while the headgroup lies similar to 11-12 angstrom from one of the rims; the structure where the polar head lies near the primary rim is the most stable. The analysis of the free energy of encapsulation of 1-butyl-3-methylimidazolium shows two minima for each insertion pathway, each of them associated with configurations where the imidazolium head lies close to one of the polar rims. As such, the most stable structure corresponds to one where the hydrophobic tail lies embedded within the cyclodextrin, while its head is localized near the secondary rim. The results are interpreted in terms of a simple model which captures the essential features that control the encapsulation process. A comparison with available experimental data is presented.