Wash grapes. Drain thoroughly on paper towels for several hours. Line a cookie sheet with parchment or waxed paper; set aside.
In a small saucepan combine milk chocolate, semisweet chocolate, and shortening. Heat and stir over low heat until chocolate is melted. Holding grape bunch by stem, dip grapes partially into melted chocolate. If necessary, spoon chocolate over grapes to coat. Let excess chocolate drip off. Place grapes, stem side up, on prepared cookie sheet.
Chill until chocolate is firm, about 30 minutes or up to 6 hours.