Put cherries in small bowl. Heat orange liqueur almost to boiling. Pour hot liqueur over cherries. Set aside until liquid is absorbed.
Preheat oven to 350°F. In a small saucepan over low heat, melt butter, then stir in cinnamon. Arrange pears in an ungreased 13-inch x 9-inch baking dish, cut-side-up. Brush pears with some of the cinnamon butter, and spoon some softened cherries into each pear half.
Bake pears, uncovered, 30 to 35 minutes, or until fork-tender, brushing occasionally with cinnamon butter. (Can be made up to 1 day ahead to this point if covered and refrigerated. Before serving, bake at 325°F 15 minutes, or until heated through.)
In a medium saucepan over medium heat, combine sugars, corn syrup, cream, and salt. Heat to boiling, reduce heat to low, and cook until mixture reaches 238°F* on a candy thermometer or until it forms a soft ball when a small amount is dropped into cold water. (Can be made up to 1 week ahead to this point if covered and refrigerated. Warm over low heat before serving.)
To serve, spoon some warm caramel sauce onto a small plate. Arrange 2 pear halves on top of sauce and drizzle with a bit more sauce.
If you live in a high-altitude area, reduce the goal temperature by two degrees for every 1000 feet above sea level. For example, if you live at 5000 feet, this caramel sauce will reach the soft ball stage at around 228°F.