We report molecular dynamics simulation results of equilibrium and dynamical characteristics pertaining to the solvation of the dye coumarin 153 (C153) trapped within hydrophobic cavities of di- and trimethylated beta-cyclodextrins (CD) in aqueous solutions. We found that stable configurations of the encapsulated probe are characterized by a slanted docking, in which the plane of the C153 lies mostly parallel to one of the glucose units of the CD. "In and out" dynamical modes of the encapsulated probe present very small amplitudes. The rotational dynamics of the trapped coumarin can be cast in terms of a simple model that includes diffusive motions within a local restrictive environment coupled to the overall rotational motion of the CD. We have examined the early stages of the solvation response of the environment following a vertical excitation of the probe. Regardless of the degree of CD methylation, the water dynamical response seems to be completed within 2-3 ps and does not differ substantially from that observed for nonencapsulated probes. The CD response is characterized by a single, subpicosecond relaxation that involves intramolecular motions. We also explored dynamical modes that could account for the recently reported persistence of Stokes shifts in the nanosecond time domain. In all cases, the only sources of ultraslow dynamics that we detected were those associated with gauche-trans interconversions in primary hydroxyl chains of the CD, which do not seem to be directly connected to the electronic excitation of the probe.