Bring a pot of water to a boil and cook the tortellini according to the package instructions, draining them 1 to 2 minutes before indicated on the package to keep them very al dente. Cool to room temperature before assembling.
To assemble, start with a cherry tomato to hold everything securely on the skewer. Then add a tortellini, a slice of salami folded in quarters, another tortellini, an artichoke half, tomato, tortellini, salami slice and finally, another tortellini. Repeat with the remaining skewer ingredients.
In a small bowl, whisk together the Italian dressing and mayonnaise. Arrange the skewers on a platter, drizzle with the dressing and serve.