The encounter of a Ca2+ ion with a protein and its subsequent binding to specific binding sites is an intricate process that cannot be fully elucidated from experimental observations. We have applied Molecular Dynamics to study this process with atomistic details, using Calbindin D9k (CaB) as a model protein. The simulations show that in most of the time the Ca2+ ion spends within the Debye radius of CaB, it is being detained at the 1st and 2nd solvation shells. While being detained near the protein, the diffusion coefficient of the ion is significantly reduced. However, due to the relatively long period of detainment, the ion can scan an appreciable surface of the protein. The enhanced propagation of the ion on the surface has a functional role: significantly increasing the ability of the ion to scan the protein's surface before being dispersed to the bulk. The contribution of this mechanism to Ca2+ binding becomes significant at low ion concentrations, where the intervals between successive encounters with the protein are getting longer. The efficiency of the surface diffusion is affected by the distribution of charges on the protein's surface. Comparison of the Ca2+ binding dynamics in CaB and its E60D mutant reveals that in the wild type (WT) protein the carboxylate of E60 function as a preferred landing-site for the Ca2+ arriving from the bulk, followed by delivering it to the final binding site. Replacement of the glutamate by aspartate significantly reduced the ability to transfer Ca2+ ions from D60 to the final binding site, explaining the observed decrement in the affinity of the mutated protein to Ca2+.