We report a molecular dynamics study on the solvation of M+ (Na+ to Cs+) alkali cations and of their LM+ complexes with a calix[4]arene host (L = 1,3-dimethoxy-calix[4]arene-crown-6 in the 1,3-alternate conformation) in the [BMI][PF6] and [BMI][Tf2N] room-temperature ionic liquids '' ILs '' based on the BMI+ (1-butyl-3-methylimidazolium) cation. The comparison of the two liquids and the dry versus humid form of the former one (with a 1:1 ratio of H2O and BMI+PF6- species) reveals the importance of humidity: in [BMI] [PF6]-dry as in the [BMI] [Tf2N] liquid, the first solvation shell of the '' naked '' M+ ions is composed of solvent anions only (four PF6- anions, and from four to five Tf2N- anions, respectively, quasi-neutralized by a surrounding cage of BMI+ cations), while in the [BMI] [PF6]-humid IL, it comprises from one to three solvent anions and about four H2O molecules. In the LM+ complexes, the cation is shielded from solvent, but still somewhat interacts with a solvent anion in the dry ILs and with water in the humid IL. We also report tests on M+ interactions with solvent anions PF6- and Tf2N- in the gas phase, showing that the AMBER results are in satisfactory agreement with QM results obtained at different levels of theory. The question of ion recognition by L is then examined by free energy perturbation studies in the three liquids, predicting a high Cs+/Na+ selectivity upon liquid extraction from an aqueous phase, in agreement with experimental results on a parent calixarene host. A similar Cs+/Na+ selectivity is predicted upon complexation in a homogeneous IL phase, mainly due to the desolvation energy of the free cations. Thus, despite their polar character, ionic liquids qualitatively behave as classical weakly polar organic liquids (e.g., choroform) as far as liquid-liquid extraction is concerned but more like polar liquids (water, alcohols) as far as complexation in a single phase is concerned.