We apply two recently developed computational methods, DFTB3 and VALBOND, to study copper oxidation/reduction processes in solution and protein. The properties of interest include the coordination structure of copper in different oxidation states in water or in a protein (plastocyanin) active site, the reduction potential of the copper ion in different environments, and the environmental response to copper oxidation. The DFTB3/MM and VALBOND simulation results are compared to DFT/MM simulations and experimental results whenever possible. For a copper ion in aqueous solution, DFTB3/MM results are generally close to B3LYP/MM with a medium basis, including both solvation structure and reduction potential for Cu(II); for Cu(I), however, DFTB3/MM finds a two-water coordination, similar to previous Born-Oppenheimer molecular dynamics simulations using BLYP and HSE, whereas B3LYP/MM leads to a tetrahedron coordination. For a tetraammonia copper complex in aqueous solution, VALBOND and DFTB3/MM are consistent in terms of both structural and dynamical properties of solvent near copper for both oxidation states. For copper reduction in plastocyanin, DFTB3/MM simulations capture the key properties of the active site, and the computed reduction potential and reorganization energy are in fair agreement with experiment, especially when the periodic boundary condition is used. Overall, the study supports the value of VALBOND and DFTB3(/MM) for the analysis of fundamental copper redox chemistry in water and protein, and the results also help highlight areas where further improvements in these methods are desirable.