Drain apricot halves, reserving 2 tablespoons syrup. Place apricots, mustard and reserved syrup in container of food processor. Process until smooth. Pour apricot sauce into a bowl.
Heat coals in grill to medium low. Place grill rack 4 inches above coals. Or, heat indoor broiler. Place Cornish Hens on grill rack or if broiling, on broiling pan, skin side down, grill or broil for 12 minutes. Turn hens and grill 12 minutes on the other side.
Sprinkle hens with half of salt, brush with some apricot sauce. Turn and grill 10 to 12 minutes longer or until well browned. Sprinkle with remaining salt and brush with more apricot sauce. Turn and grill 10 to 12 minutes longer or until hens are cooked thoroughly. Serve with remaining sauce.
