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For a class of highly frustrated antiferromagnetic quantum spin lattices theground state exhibits a huge degeneracy in high magnetic fields due to theexistence of localized magnon states. For some of these spin lattices (inparticular, the 1D dimer-plaquette, sawtooth and kagom\'{e}-like chains as wellas the 2D kagom\'{e} lattice) we calculate rigorously the ground-state entropyat the saturation field. We find that the ground-state entropy per site remainsfinite at saturation. This residual ground-state entropy produces a maximum inthe field dependence of the isothermal entropy at low temperatures. Bynumerical calculation of the field dependence of the low-temperature entropyfor the sawtooth chain we find that the enhancement of isothermal entropy isrobust against small deviations in exchange constants. Moreover, the effect ismost pronounced in the extreme quantum case of spin 1/2

Finite low-temperature entropy of some strongly frustrated quantum spin lattices in the vicinity of the saturation field