Using kitchen shears, trim sharp tips of artichoke leaves. Remove any small leaves from bottoms of artichokes; trim stems. Using a serrated knife, cut off top quarter of each artichoke.
Fill a 10-inch steamer with enough water to come about 2 inches up sides. (Alternatively, use a pot with a steamer insert.) Add a pinch of salt and the tarragon sprig. Bring to a boil. Place artichokes upright in steamer. Cover, and reduce heat; simmer until bottoms of artichokes are very tender when pierced to the center with the tip of a paring knife, 35 to 50 minutes. (Add more hot water if needed to maintain level.)
Before serving, melt butter in a small saucepan over low heat; stir in chopped tarragon, and season with salt. Serve artichokes with lemon wedges and warm tarragon butter for dipping.
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