Human carbonic anhydrase (hCA, EC 4.2.1.1) isoforms IX and XII are overexpressed in solid hypoxic tumors, and they are considered as prognostic tools and therapeutic targets for cancer. Based on a molecular simplification of the well-known coumarin scaffold, we developed a new series of derivatives of the pyran-2-one core. The new compounds are endowed with potent and selective inhibitory activity against the tumor-related hCA isoforms IX and XII, in the low nanomolar range, whereas they are inactive against the two cytosolic off-targets hCA I and II. The compounds exhibiting the best hCA inhibition were further investigated against the breast adenocarcinoma cell line (MCF7) in hypoxic conditions, evaluating their ability to eventually synergize with doxorubicin. The compounds’ biocompatibility on healthy cells was also tested and confirmed on Human Gingival Fibroblasts (HGFs). Furthermore, the possible binding mode of all compounds to the active site of the tumor-associated human CA IX was investigated by computational techniques which predicted the binding conformations and the persistency of binding poses within the active site of the enzyme, furnishing relevant data for the design of tight binding inhibitors.