A pigment from the edible mushroom Xerocomus badius norbadione A, which is a natural derivative of pulvinic acid, was found to possess antioxidant properties. Since the pulvinic acid represents a novel antioxidant scaffold, several other derivatives were recently synthetized and evaluated experimentally, along with some structurally related coumarine derivatives. The obtained data formed the basis for the construction of several quantitative structure-activity and pharmacophore models, which were employed in the virtual screening experiments of compound libraries and for the prediction of their antioxidant activity, with the goal of discovering novel compounds possessing antioxidant properties. A final prioritization list of 21 novel compounds alongside 8 established antioxidant compounds was created for their experimental evaluation, consisting of the DPPH assay, 2-deoxyribose assay, β-carotene bleaching assay and the cellular antioxidant activity assay. Ten novel compounds from the tetronic acid and barbituric acid chemical classes displayed promising antioxidant activity in at least one of the used assays, that is comparable to or even better than some standard antioxidants. Compounds 5, 7 and 9 displayed good activity in all the assays, and were furthermore effective preventers of oxidative stress in human peripheral blood mononuclear cells, which are promising features for the potential therapeutic use of such compounds.