The Raman spectra of H(2) and HD molecules in simple hydrogen and binary hydrogen-tetrahydrofuran clathrate hydrates have been measured at temperatures as low as 20 K. The rotational bands of trapped molecules in simple and binary hydrates have been analyzed, and the contributions originating from hydrogen molecules in the large cages have been separated from those in the small cages. A theoretical model, consisting in rigid cages enclosing interacting hydrogen molecules, has been exploited to calculate, on the basis of quantum mechanics, the Raman intensity of the rotational transitions for up to two interacting molecules in one cage. A comparison with experiment leads to a clear interpretation of sidebands appearing in the Raman rotational lines. The quantitative agreement between theory and experiment obtained in some cases clarifies the importance of the choice of the interaction potential, and of the proton disorder in the clathrate crystal.