A computational protocol for the treatment of hindered rotations in the vibrational averaging of molecular properties is described. As examples, the specific rotations [alpha]D of (R)-methyloxirane, (1S)-methylnorbornanone, and (S)-epichlorohydrin and the spin-spin coupling constant J(HD) for [Ir(Cp)(PMe3)H2]+ are investigated. For each of the four molecules, the relaxed and unrelaxed potential energy surfaces along the rotational coordinate of interest are used to solve the nuclear Schrödinger equation using a pseudospectral method. Analysis of the results demonstrate that the vibrational averaging for low-frequency modes that represent hindered rotations can lead to unphysical behavior at high temperatures while simply neglecting the rotational contributions is also not desirable. The method described in this work connects the (an)harmonic oscillator behavior at low temperatures with the free rotor-like behavior at high temperatures.