Cook the tortellini according to the package directions. Drain and let cool completely.
In a large bowl, toss the cooled tortellini with pesto and olive oil.
Add tomatoes, mozzarella, salt, and pepper. Stir gently so you don't tear the pasta.
Thread 2 to 3 tortellini, 2 tomato halves, and 1 mozzarella ball onto each small skewer, repeating until the tortellini are used; the exact count will vary with the pasta brand and size.
Store covered in the refrigerator until ready to serve. Keep chilled or serve in small batches, and do not leave the bites at room temperature for more than 2 hours (1 hour above 90°F).