Wash the watermelon, dry it and peel off the green skin, then discard. Slice the white part of the rind into ¼ inch cubes.
Wash oranges, cut them into slices, and then cut each slice into smaller pieces.
Combine watermelon, orange slices, brown sugar, water, and ginger in a medium pot over medium-high heat. Bring to a boil, reduce heat to simmer for 1 hour and 20 minutes, stirring occasionally.
Mash some of the watermelon and orange rinds. To check if the jam has been set, remove a spoonful and see how it drips off the spoon; if it is runny and thin, then it needs more time to cook. If it is thick and dense, then it is ready.