Clean, wash and dry grate the tomatoes. Cut ham and salami slices in half lengthwise. Drain mozzarella balls and let them drain. Wrap 1/4 of the mozzarella balls with ham and 1/4 of the balls with salami. Wash the basil, shake dry and pluck the leaves from the stalks.
Shorten skewers. Place 2 mozzarella balls, 2 tomatoes and basil alternately on each skewer. Arrange on a plate and drizzle with olive oil. Season with coarse salt and pepper