In a medium saucepan combine water and sugar. Cook and stir over high heat until mixture comes to a boil and sugar dissolves. Remove from heat and cool syrup completely.
Place strawberries in a food processor bowl or blender container. Cover; process or blend until nearly smooth. (For best results, puree half of the mixture at a time.) In a bowl stir together pureed strawberries, rum, lime peel, lime juice, and orange liqueur. Stir in the cooled syrup.
Freeze in a 4-quart ice-cream freezer according to the manufacturers directions. Using a small ice cream scoop, scoop sorbet into dishes. Garnish with lime peel twists, if desired. Makes 2 quarts or 16 servings.