In a hot pan, carefully blister half the cherry tomatoes and shishito peppers.
Cut the remaining cherry tomatoes in half.
Combine the watermelon and all the cherry tomatoes in a large bowl. Slice the shishito peppers into quarter-inch thick strips and add to the tomatoes and watermelon.
Drizzle all the ingredients with olive oil until everything is lightly coated. Season with salt and pepper to taste.
Add all of the basil and mint to the salad and toss to incorporate evenly.