Heat the grill to medium.
Rinse anchovies in cold water and pat dry with paper towels. You can keep the head on or cut off. Toss anchovies in olive oil and season with salt and pepper.
Place anchovies on the grill, cover and grill for 3-4 minutes, then flip and cook for another 3-4 minutes until lightly charred with grill marks.
Remove and serve with lemon wedges