Wash herbs thoroughly; let dry, and place in a sterilized wide-mouthed jar. Bruise herbs, using a pestle or the back of a spoon.
Place vinegar in a medium saucepan; bring to a boil. Pour vinegar over herbs in jar. Cover with a metal lid, and screw band tight. Let stand 10 days in a warm place; shake jar daily.
Strain vinegar through 4 layers of cheesecloth into a decorative bottle, discarding herb residue. Add additional sprigs of tarragon. Seal bottle with a cork or other airtight lid.