In a small saucepan, combine the sugar, water, lemon juice, ginger, and tarragon stems. Heat until sugar has dissolved. Set aside to cool. Strain.
Combine the berries in a large serving bowl. Pour the simple syrup over the berries. Chop the tarragon leaves and add to the bowl. Toss gently to coat. Serve on cake, with whipped cream or just as is.