Rinse the cranberries; discard any that are soft, bruised, or discolored. Drain well.
In a saucepan, combine the sweetener and water. Heat over medium until the sweetener dissolves and the liquid simmers.
Add the cranberries to the pan and bring to a gentle boil.
Reduce heat to low and simmer, uncovered, stirring occasionally, until the cranberries burst and the sauce begins to thicken — about 12–15 minutes.
Taste the sauce. If it’s too tart, add a little more sweetener until it reaches your preferred sweetness.
Remove from heat and let the sauce cool. It will continue to thicken as it cools.
Serve at room temperature or cold.