Peel and cube melons, and put in gallon-sized food storage bags. Freeze overnight.
Put half cantaloupe in food processor, pur8Eeing until smooth. Pour into container, and freeze. Repeat with remaining melon.
Repeat process with honeydew melon.
Place 8 balloon wine glasses in freezer.
Put frozen cantaloupe pur8Ee in processor when frozen for at least 4 hours. Process, and place 1/4 cup pur8Ee in each of 8 chilled wine glasses. Repeat with honeydew pur8Ee. Continue layering, alternating melon pur8Ees, until each wine glass is nearly full. Freeze overnight.
To serve, garnish each wine glass or plate with a lily or other flower.