Combine first 4 ingredients in a large saucepan. Bring to a boil; reduce heat, and simmer, uncovered, 5 minutes. Strain berry mixture through a sieve into a bowl. Discard solids.
Return berry juice mixture to pan. Combine cornstarch and water; stir into juice mixture. Bring to a boil over medium- high heat, stirring constantly; cook 1 minute. Remove from heat; stir in butter and vanilla. Cool slightly.
Spoon 2 teaspoons berry juice mixture into each shell. Chill 2 hours. Top each tartlet with 2 teaspoons whipped topping and 1 blackberry or raspberry.