Heat olive oil in a medium saucepan over medium heat. Once hot, add onion and salt. Saute until onion is soft and beginning to brown, about 15 minutes. Add sugar and cinnamon; stir until sugar dissolves, about 4 minutes. Add cranberries, cherries, and cherry canning liquid.
Bring to a boil. Reduce heat to low, and simmer until most of the cranberries have popped, stirring occasionally, about 15 minutes.
Serve cold or allow to come to room temperature.
The cranberry sauce can be made 3 days ahead and kept refrigerated.
Cook's Notes: *I used a container of organic cranberries that came in a 7.5 oz box. If you can't find this size, grab a bag of fresh cranberries (these are usually 12 oz). Take a little more than half of the bag. The sauce will still be great even if you have a little more or a little less cranberries. And, if you can't find fresh, frozen whole cranberries will work as well. **I used Oregon Fruit Products Brand for the tart cherries packed in water. If you can't find these, I can usually find tart cherries packed in syrup from other brands. Drain the syrup off of the cherries (this makes a great sorbet if you freeze it), and use the drained cherries. Instead of the cherry canning liquid, use water in its place. If you can't find canned cherries at all, frozen will also work.
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