Preheat the grill, setting the burners to medium-high. Oil the grate.
Spread a little pesto on one side of each tomato slice. Place them, seasoned side down, on the hot grill. Grill for about 1 minute, just to mark them. Turn over and cover with a little pesto. Grill for about 1 minute to mark the other side. Use approximately 15 ml (1 tablespoon) of pesto on each tomato slice.