Wash and dry the cranberries. Make sure to check the cranberries for any stems or bad cranberries and remove. (Nothing ruins a good sauce like branches in it!)
In a medium-sized saucepan over medium heat, dissolve both sugars in the orange and cranberry juices.
Once the sugar is dissolved, stir in the cranberries and a pinch of salt. Bring the mixture to a boil over medium heat and then reduce to a simmer. Stir to blend and simmer for an additional 7-12 minutes. (Watch carefully, as the sauce can bubble up a bit!) Some of the cranberries will burst and some will remain whole -- you can mash up more cranberries as desired. (If the sauce is thickening too quickly, lower the temperature a bit, and alternatively, if it isn't thickening, increase the temperature a bit.)
Remove from heat and place sauce in a bowl. Cranberry sauce will thicken more as it cools. Store for up to a week in an airtight container in the fridge.