Place white chocolate pieces in a small heavy saucepan; melt slowly over low heat. Cool slightly and transfer to a small deep bowl.
Line a baking sheet with waxed paper. Holding onto the stem end, dip strawberries one at a time in the white chocolate three-quarters of the way up to the stem. Place on the wax paper and refrigerate for about 10 minutes.
Meanwhile, slowly melt dark chocolate in a small heavy saucepan. Remove strawberries from the refrigerator and dip in the dark chocolate, leaving part of the white chocolate showing. Return to the refrigerator to chill.