The concept of maximum occurrence (MO), i.e., the maximum percent of time that flexible proteins can spend in any given conformation, is introduced, and a rigorous method is developed to extensively sample the conformational space and to construct MO maps from experimental data. The method is tested in a case study, the flexible two-domain protein calmodulin (CaM), using SAXS and NMR data (i.e., pseudocontact shifts and self-orientation residual dipolar couplings arising from the presence of paramagnetic lanthanide ions), revealing that the "closed" and "fully extended" conformations trapped in the crystalline forms of CaM have MOs of only 5 and 15%, respectively. Compact conformations in general have small MOs, whereas some extended conformations have MO as high as 35%, strongly suggesting these conformations to be most abundant in solution. The method is universally applicable as it requires only standard SAXS data and specific NMR data on lanthanide derivatives of the protein (using native metal sites or lanthanide tagging). The computer program is publicly available using the grid computing infrastructure through the authors' Web portal.