An efficient microwave-assisted method of synthesis of some novel 2-arylidene-2H-furo[2,3-f]chromen-3(7H)-ones 6a-j in excellent yields was described and structural assignment of the products was confirmed on the basis of IR, H-1 NMR, C-13 NMR, MS, and analytical data. The synthesized compounds were screened for antioxidant activity using 2,2-diphenyl-1-picrylhydrazyl and hydrogen peroxide radicals. The compounds 5d, 5h, 6a, 6e, and 6j exhibited better radical scavenging ability. Antimicrobial activity results demonstrated that compounds 5b, 5e, 6b, 6c, and 6e showed promising antimicrobial potency. The in silico molecular docking studies were also carried out for the inhibition of cyclooxygenase-II enzyme. These molecular docking results were well complemented to the antioxidant activity studies.