For simple syrup, in a small saucepan bring 1 cup water and the sugar to boiling, stirring to dissolve sugar. Reduce heat. Simmer, uncovered, for 3 minutes. Remove from heat. Place in refrigerator to cool.
Meanwhile, for puree, in food processor combine the 1 pint raspberries, pear, lime juice, pear liqueur, and salt. Cover; process 30 seconds or until smooth. Strain mixture through a fine-mesh sieve to remove seeds; discard seeds. Stir in chilled simple syrup.
Spread mixture in an 8x8x2-inch baking pan. Cover; freeze 4 hours or until solid. Break up mixture with a fork; place in food processor. Cover; process 30 seconds or until smooth. Transfer to 1-quart freezer container; cover and freeze sorbet 6 to 8 hours or until solid. To serve, let stand at room temperature 5 minutes before scooping. Serve with additional raspberries. Makes 6 (1/2-cup) servings