The reorientational relaxation times of some small aromatic solutes are determined with nuclear magnetic resonance spectroscopy and time-resolved fluorescence anisotropy measurements in various solvents that exhibit viscoelasticity in the megahertz region. All the reorientational relaxation times in viscoelastic liquids are shorter than those predicted by the hydrodynamic Stokes-Einstein-Debye (SED) relation using the steady-states-hear viscosity. The deviation from the SED relation becomes larger in solvents whose shear relaxation is slower. When the reorientational relaxation times in a solvent are compared, the deviation from the SED relation tends to decrease when the reorientational relaxation time increases. From a comparison with the shear relaxation spectra, it is demonstrated that the deviation from the SED relation can be ascribed to the effective reduction of the viscous friction on fast reorientation, reflecting the decrease in shear viscosity with increasing frequency.