The proper description of low-spin states of open-shell systems, which are commonly encountered in the field of bioinorganic chemistry, rigorously requires using multireference ab initio methodologies. Such approaches are unfortunately very CPU-time consuming as dynamic correlation effects also have to be taken into account. The broken-symmetry unrestricted (spin-polarized) density functional theory (DFT) technique has been widely employed up to now to bypass that drawback, but despite a number of relative successes in the determination of singlet-triplet gaps, this framework cannot be considered as entirely satisfactory. In this contribution, we investigate some alternative ways relying on the spin-flip time-dependent DFT approach [Y. Shao et al. J. Chem. Phys. 118, 4807 (2003)]. Taking a few well-documented copper-dioxygen adducts as examples, we show that spin-flip (SF)-DFT computed singlet-triplet gaps compare very favorably to either experimental results or large-scale CASMP2 computations. Moreover, it is shown that this approach can be used to optimize geometries at a DFT level including some multireference effects. Finally, a clear-cut added value of the SF-DFT computations is drawn: if pure ab initio data are required, then the electronic excitations revealed by SF-DFT can be considered in designing dramatically reduced zeroth-order variational spaces to be used in subsequent multireference configuration interaction or multireference perturbation treatments.