Place 1 1/2 cups of watermelon, honeydew melon & cantaloupe in a 2 quart/2L (or large jug or screw-top jar (I used a big Mason jar).
Take the 2 cups of watermelon & push them through a fine metal strainer using a ladle or the back of a large metal spoon, catching the watermelon juice in a bowl or jug. Repeat with remaining chopped watermelon. You will need 2 to 3 cups of juice; discard solids. Add the juice to the jar.
Add wine, orange liqueur & rum; stir to combine. Seal the jar, or cover the jug, & chill for 4 hours or overnight.
To serve, place ice in glasses, half to two thirds fill glasses with melon sangria, adding some chopped melon or melon balls, & top-up glasses with cold ginger ale. Serve immediately, adding a fruit garnish if desired. Makes 1 1/2 to 2 quarts/2L.