Place a rack in center of oven and preheat oven to 350°F. Sift together flour, cocoa, baking powder and salt. Using an electric mixer, cream butter and sugar on high speed until light and fluffy, about 3 minutes. Add eggs 1 at time, mixing well after each addition; then add melted chocolate. With mixer on low, gradually add dry ingredients to chocolate mixture. Stir in white chocolate and cherries.
Drop heaping tablespoonfuls of dough onto an ungreased baking sheet, spacing them 2 inches apart. Bake cookies until set, 10 to 12 minutes. Let cool slightly; then transfer to a wire rack and let cool completely.