Coumarin derivatives are a peculiar class of inhibitors of the family of metalloenzymes carbonic anhydrases (CA, EC 4.2.1.1). Several coumarins display higher affinity and selectivity toward most relevant and druggable CA isoforms. By decorating the natural compound umbelliferone (1) we have identified a new series of coumarin-based compounds demonstrating high CA inhibitory effects with nanomolar affinity for hCA IX and hCA XII isoforms that were considered a target amenable to develop antitumor agents. The most active tested compounds proved to be potent inhibitors with Ki values equal to that of the well-known inhibitor acetazolamide (AAZ), that lacks selectivity over ubiquitous hCA I and hCA II. As suggested by docking studies the coumarins, that are lacking of the canonical metal binding groups, do not interact with Zinc ion within the catalytic site as found for classical sulfonamide type inhibitors of CAs. Thus, the studied inhibitors might possess a non-classical inhibitory mode of action preventing the carbon dioxide to entry into catalytic cavity and its conversion into bicarbonate ion. Specifically, the most active inhibitor of hCA XII compound 18i (Ki value of 5.5 nM) and its supposed hydrolytic products could establish a web of H-bond interactions within the enzymatic cavity.