Trim off the ends of the zucchini and cut it in half lengthwise. Using small spoon, scrape out just a bit of zucchini flesh, to create a well (just enough to create a place to cradle your mozzarella cheese), leaving about 1/4" from the edge intact.
Brush the cut side of the zucchini with olive oil and season with salt (I also added pepper).
Place zucchini, cut side down, on the grill at an angle. Continue cooking until the zucchini is charred and beginning to soften, about 10 minutes or so.
Turn zucchini over, laying the zucchini in the same direction as the lines on the rack, as this will help to cradle each zucchini boat. Plac 2 mozzarella strips into the well area of each zucchini boat.
Top the mozzarella with about 8 tomato pieces. Cover the lid on the grill and continue cooking until the cheese is melted. After the cheese is melted, remove your zucchini boats carefully from the grill.