Bring a large pot of salted water to a boil. Cook the ziti according to package directions. Drain and reserve.
While the pasta is cooking, prepare the calamari. Heat a grill pan or outdoor grill over high heat. Pat dry and sprinkle with salt and pepper. Toss with vegetable oil.
Grill calamari for 1 minute per side or until nicely charred and just cooked through. Remove to a cutting board and slice into ¼” rings.
Place the ziti, calamari and celery in a bowl. Toss with the parsley, lemon juice and olive oil. Season to taste with salt and pepper.