In a saucepan over low heat, warm the sugar and the orange juice, stirring constantly, until the sugar dissolves.
Meanwhile, rinse the cranberries in a colander.
Add the cranberries to the pan and cook over low heat for 10 minutes. Remove the pan from the heat and let cool.
Once cool, pour the mixture into a blender and purée it. Strain the mixture into a pitcher, discarding any solids. (You can cover and stash it in the fridge until ready to use. It will thicken as it cools, so you’ll need to stir it just prior to using.)
For each margarita, put some crushed ice, 1 to 1 1/2 ounces tequila, 1/2 ounce Grand Marnier, and 2 ounces cranberry purée in a shaker. Shake well.
To serve, pour the margarita into a sugar-rimmed margarita or martini glass. Add a cranberry swizzle stick and/or an orange twist for garnish.