Place pork in a large, heavy self-sealing plastic bag set in a shallow dish; set aside.
For marinade, in a small bowl combine the ketchup, soy sauce, brown sugar, wine or lime juice, ginger, and garlic. Remove 3/4 cup of the mixture to a small bowl; cover and chill until needed. Pour remaining mixture over pork; seal bag. Marinate in refrigerator for 4 to 24 hours, turning bag occasionally.
Drain pork, reserving marinade. For a charcoal grill arrange hot coals around a drip pan. Test for medium-high heat above the pan. Place pork on grill rack over pan. Cover and grill 20 minutes. Brush with drained marinade. Cover and grill 15 to 20 minutes more or until an instant-read thermometer registers 155 degrees F when inserted into the thickest part of the meat. (For a gas grill, preheat grill. Reduce heat to medium-high. Adjust for indirect cooking. Grill as above.) Remove pork from grill. Cover pork with foil and let stand 10 minutes before slicing. (The meat's temperature will rise 5 degrees F during standing.)
Meanwhile, place reserved sauce mixture in a small saucepan; heat through. Pass sauce with pork. Garnish with lime wedges and fresh herbs. Makes 8 servings.