Brønsted-acid zeolites are currently being used as catalysts in a wide range of technological processes, spanning from the petrochemical industry to biomass upgrade, methanol to olefin conversion and the production of fine chemicals. For most of the involved chemical processes, acid strength is a key factor determining catalytic performance, and hence there is a need to evaluate it correctly. Based on simplicity, the magnitude of the red shift of the O-H stretching frequency, Δν(OH), when the Brønsted-acid hydroxyl group of protonic zeolites interacts with an adsorbed weak base (such as carbon monoxide or dinitrogen) is frequently used for ranking acid strength. Nevertheless, the enthalpy change, ΔH(0), involved in that hydrogen-bonding interaction should be a better indicator; and in fact Δν(OH) and ΔH(0) are often found to correlate among themselves, but, as shown herein, that is not always the case. We report on experimental determination of the interaction (at a low temperature) of carbon monoxide and dinitrogen with the protonic zeolites H-MCM-22 and H-MCM-56 (which have the MWW structure type) showing that the standard enthalpy of formation of OH···CO and OH···NN hydrogen-bonded complexes is distinctively smaller than the corresponding values reported in the literature for H-ZSM-5 and H-FER, and yet the corresponding Δν(OH) values are significantly larger for the zeolites having the MWW structure type (DFT calculations are also shown for H-MCM-22). These rather unexpected results should alert the reader to the risk of using the O-H frequency shift probed by an adsorbed weak base as a general indicator for ranking zeolite Brønsted acidity.