Thaw shrimp, if frozen. Peel and devein shrimp, leaving tails intact. Rinse shrimp; pat dry with paper towels. In a small bowl stir together mayonnaise, tomato paste, lemon juice, and garlic. Cover and chill until ready to serve.
Brush both sides of each shrimp with melted butter. Sprinkle both sides of each shrimp with Cajun seasoning. Place on the unheated rack of a broiler pan.
Broil 4 to 5 inches from the heat for 2 minutes. Turn shrimp; broil for 1 to 2 minutes more or until shrimp are opaque. Serve shrimp with mayonnaise mixture. Makes 8 appetizer servings.