The ability of hybrid, nonhybrid and meta-GGA density functional theory (DFT) based methods (B3LYP, BP86, M06 and M06L) to provide reliable structures and thermochemical properties of biochemically important Cu(I)/(II)···ESH (ergothioneine) and ···OSH (ovothiol) has been assessed. For all functionals considered, convergence in the optimized structures and Cu(I)/(II)···S/N bond lengths is only obtained using the 6-311+G(2df,p) basis set or larger, with the nonhybrid DFT method BP86 appearing, in general, to provide the most reliable structures. The reduction potentials associated with the reduction of Cu(II) to Cu(I) when complexed with either OSH and ESH were also determined. The implications for their ability to thus help protect against Cu-mediated oxidative damage are discussed. Importantly, the binding of OSH and ESH with Cu ions disfavors Cu(I)/Cu(II) recycling by increasing the reduction potential for the Cu(II) to Cu(I) reduction and as a result, inhibits the potential oxidative damage caused by such Cu ions.