various methods employed for characterizing complex ions in solution, among the most direct is that of Raman spectroscopy. This method determines the vibrational spectrum of the complex species with a minimum of interference from the solvent and from other species present in the solution.
In addition to the techniques that have already been discussed, epr, magnetic measurements by squid and also exafs can be used. The latter is more difficult to access. Regarding NMR, if the metal ion is paramagnetic, the paramagnetic NMR technique should be used.
It is very easy to discuss and very difficult to analyze the geometry of the metal complexes. There are so many studies such as UV, IR, NMR, Mass, XRD, Raman, ESR and Cyclovoltametry. Also you may proceed for theoretical studies like DFT, Quantum chemical studies and MEP.