New pyranocoumarin and coumarin-sulfonamide derivatives were prepared and evaluated for their antioxidant, antimicrobial, and/or anti-inflammatory activities. Coumarin-sulfonamide compounds 8a–d demonstrated significant antioxidant activity, while 7c,d, 8c,d, and 9c,d exhibited antimicrobial activity equal to or higher than the standard antimicrobials against at least one tested microorganism. Regarding the anti-inflammatory testing, pyranocoumarins 2b, 3a,b and 5c and coumarin-sulfonamide compound 9a showed more potent antiproteinase activity than aspirin in vitro; however, five compounds were as potent as aspirin. The anti-inflammatory activity of the promising compounds was further assessed pharmacologically on formaldehyde-induced rat paw oedema and showed significant inhibition of oedema. For in vitro COX-inhibitory activity of coumarin derivatives, pyranocoumarin derivative 5a was the most selective (SI = 152) and coumarin-sulfonamide derivative 8d was most active toward COX-2 isozyme. The most active derivatives met the in silico criteria for orally active drugs; thus, they may serve as promising candidates to develop more potent and highly efficient antioxidant, antimicrobial, and/or anti-inflammatory agents.