We present a general theoretical framework suitable for an economical, but rigorous, analysis of the relaxivity and EPR data of paramagnetic metal complexes. This framework is based on the so-called Grenoble method that properly accounts for the fluctuations of the “static” zero-field splitting Hamiltonian and avoids the misinterpretation of experimental data, which occurs with the Solomon, Bloembergen, and Morgan (SBM) formalism and may lead to erroneous conclusions. The applicability of the SBM approximation is discussed. Our approach is implemented in the case of a new Gd3+ chelate with a cyclodextrin derivative ligand hexakis(2-O-carboxymethyl-3,6-anhydro)-α-cyclodextrin (ACX), designed to obtain lanthanide complexes of enhanced stability in comparison to natural cyclodextrins. The introduction of carboxymethyl units on the six residual hydroxyl groups of an α-per-3,6-anhydro cyclodextrin leads to mono- and binuclear Ln3+ complexes with log β110 ≈ 7.5. The GdACX complex induces large water proton relaxivity in 0.1 M KCl aqueous solution. The molecular parameters governing the longitudinal (r1) and transverse (r2) relaxivities above 1 T are obtained through simple SBM-like theoretical expressions and complementary experimental techniques. The metal hydration state, the translational diffusion coefficient of the complex, and its rotational correlation time are derived from luminescence lifetime studies, pulse-field gradient NMR, and deuteron quadrupolar relaxation, respectively. The high relaxivity induced by the GdACX complex is attributed to its high hydration state in the presence of potassium ions and to a rotational correlation time lengthened by the hydrophilic character of the ACX scaffold.