Add the oil to a wide pan and heat to about 325 degrees F. Preheat the oven to 200 degrees F. Pat the calamari dry with paper towels.
Combine the flour and cayenne pepper. Working in batches, toss 1/3 of the calamari in the seasoned flour. Transfer the calamari to a mesh strainer and shake off the excess flour.
Carefully drop the calamari into the hot oil; the oil should bubble gently and the calamari should have plenty of room to swim around and fry gently. Do not crowd the pan or the oil won't come back up to temperature quickly. When done, the calamari should be very pale golden and tender. It should not look like little brown rubber bands. Remove the calamari from the hot oil and drain it on paper towels. Salt it immediately and keep it warm in the oven until all the calamari is done.
Repeat in 2 more batches with the remaining calamari.