Cyclic ozone (O-3) has not been isolated so far, despite its computed kinetic persistence. Possibilities of "trapping" this molecule (or the valence-isoelectronic cyclic thiozone, S-3) in transition metal complexes are investigated in this paper. Candidates were constructed, first using the 18-electron rule as a guide and then optimizing the structures with the DFT-B3LYP method. A variety of structures result: oxo-peroxo species, di-sigma- and pi-bonded open ozone complexes, some eta(1) and eta(2) cyclic ozone complexes, and a few bona fide eta(3) Cyclic O-3 and S-3 complexes. MLn fragments suitable for complex formation would need to contain very strong pi-acceptor ligands. Nitrosyl ligands were chosen to minimize an energy mismatch between the O-3 donor orbitals and the MLn acceptor orbitals. On this basis, the existence of the complexes [S3W(NO)(3)](3+), [O3M(NO)(3)](3+) (M = Cr, Mo, W, Fe, Ru, Os), and [S3W(NO)(2)(Co)](2+) containing cyclic O-3 and S-3 is suggested. In another approach, facing up to the oxidizing power of O-3, potential systems were built from late transition metals in high oxidation states, and also do early transition metal centers.