Stir together sugar, port, and 3/4 cup water in a heavy 3-qt. saucepan until blended.
Add cranberries; bring to a boil, and cook over medium-high heat, stirring often, 8 to 10 minutes or until cranberry skins begin to split.
Remove from heat, and let cool 15 minutes.
Pulse cranberry mixture in a food processor 3 to 4 times or until cranberries are almost pureed; stir in orange liqueur. Cover and chill 8 hours before serving. Store in refrigerator in an airtight container up to 3 weeks.
Note: We tested with Grand Marnier for orange liqueur.
