In a small food processor, combine the cilantro, ginger and garlic; cover and process until cilantro and garlic are chopped. While processing, gradually add oil and lemon juice in a steady stream until smooth. Transfer to a small serving bowl; set aside.
Thread shrimp onto four metal or soaked wooden skewers. Sprinkle with lemon-pepper. Moisten a paper towel with cooking oil; using long-handled tongs, lightly coat the grill rack.
Grill, covered, over medium heat or broil 4 in. from the heat for 6-8 minutes or until shrimp turn pink, turning once. Serve with cilantro sauce.