Hydrogen bonds are fundamental to molecular structure and function across chemistry, biology, and materials science. Accurate characterization of hydrogen bond geometry, strength, and spectroscopic properties remains a central challenge, particularly for strong hydrogen bonds where quantum delocalization of the bridging proton is significant. In this work, we develop and validate a computational protocol that explicitly accounts for proton delocalization by solving the one-dimensional Schrödinger equation along the proton transfer coordinate for a diverse set of NHN, OHO, and NHO hydrogen-bonded complexes. Quantum mechanical averaging over the proton probability density yields geometric and spectroscopic parameters that are more representative of the true, time-averaged environment probed in experiment. We establish robust correlations between the bridging proton chemical shift and both geometric and energetic descriptors, demonstrating that accounting for nuclear quantum effects leads to more reliable and transferable spectrum-structure relationships than classical approaches. Our results highlight the necessity of including proton delocalization in theoretical descriptions of hydrogen bonds and provide a practical toolkit for the interpretation and prediction of hydrogen bonding effects in complex molecular systems.