Quantum tunneling is known to be an important process in H-transfer reactions and previous work has established that it occurs in many enzyme-catalyzed reactions. However, there is a considerable debate as to its relevance to catalysis and whether it could be harnessed by enzymes through evolution. To address these questions, we have analyzed how H-tunneling occurs in a designed enzyme, and how it changes along an evolutionary trajectory. Our results indicate that H-tunnelling is enhanced in the enzyme, by a factor of approx. 2, which is considerably less than the 10^6-fold improvement through reduction in activation energy. Additionally, tunnelling does not significantly change during evolution. Rather, fourteen crystal structures and kinetics reveal that a reduction in activation energy, as a result of optimising the conformational landscape of the enzyme underlies the improvement. These results suggest that although H-tunnelling occurs in enzymes, it is unlikely to be harnessed through evolution.