Cyclic oligomers of hexamethylene furanoate and hexamethylene terephthalate were obtained from 1,6-hexanediol and the corresponding methyl esters using Candida antarctica lipase B (CALB) enzyme catalyst. HPLC, MALDI-TOF MS, and NMR analyses showed that mixtures composed from cyclic dimer up to heptamer were obtained almost quantitatively. Subsequently, these cycles were polymerized by ring opening polymerization (ROP) mediated by CALB to obtain semicrystalline polymers. In addition, we demonstrated that the polymers obtained from the ROP process could be transformed into cyclic oligomers in high yields using enzymatic cyclodepolymerization, thereby recycling the polymer in a circular biosynthetic path.