Quantum chemical calculations were used to study the variation of NMR proton chemical shifts delta(H) along the H-transfer process N-H...O-->N...H...O-->N...H-O in two short strong hydrogen bond (SSHB) systems: the anionic complex formed by 4-methylimidazole and acetate and the neutral complex formed by 4-methylimidazolium cation and acetate. Changes Of delta(H) associated with the H-transfer were studied at the equilibrium and one shorter N...O heteroatom distances in order to investigate the influence of stronger HB effects on chemical shifts. Optimized geometries and electron densities were obtained in MP2/6-311++G(d,p) calculations, while delta(H) were computed at the B3LYP/6-311++G(d,p) level of theory. Extreme downfield shifts in the 15-20 ppm range for N-H...O and 13-18 ppm for N...H-O localized stages and maximum shifts about 23 ppm for the delocalized N...H...O state were found in agreement with data measured and computed before in SSHB systems as well as in biomolecular systems regarding enzymatic processes. These large chemical shifts that reveal extremely deshielded protons are shown to depend closely on local properties of the electron density, suggesting partially covalent features in the interaction underlying the SSHB environment.