Grate 2 teaspoons rind from orange. Save for garnish. With knife, remove remaining peel and white pith from orange. Chop orange into 1/2-inch pieces, discarding any seeds.
In nonreactive saucepan, combine orange pieces, cranberries, ginger, lemon juice, sugar and juice. Bring to a boil. Reduce heat; simmer 3 to 5 minutes, until thickened and most of berries have popped.
Transfer sauce to serving bowl. Cool, stirring occasionally; refrigerate. To serve, garnish with reserved rind.