Remove any discolored leaves and the small leaves at base of artichokes. Trim stems even with base of artichokes. Cutting straight across, slice 1 inch off tops and discard tops. Snip off points of remaining leaves with scissors. Rinse artichokes with cold water.
Place steamer basket in 1/2 inch water in 4-quart Dutch oven (water should not touch bottom of basket). Place artichokes in basket. Cover tightly and heat to boiling; reduce heat. Steam 20 to 25 minutes or until bottoms are tender when pierced with knife.
Meanwhile, melt butter; stir in rosemary and lemon juice. Pluck out artichoke leaves one at a time. Dip base of leaf into rosemary mixture.