Place ramps on grill and cook until tender and smoky, about 1 minute. Remove ramps from grill and allow to cool. Chop cool ramps into 1/4-inch pieces and place in small mixing bowl with black pepper and tomatoes. Season with salt and set aside.
Bring 6 quarts water to boil and add 2 tablespoons salt.
Roll pasta to thinnest setting and cut into 3-inch squares. Place 1 tablespoon ramp mixture in center of each square and fold into a triangle. Continue until all pasta is done. Place ravioli in boiling water and simmer until cooked, about 4 to 5 minutes.
Meanwhile, heat calamari and olive oil in a 12 to 14-inch saute pan until boiling. Lower heat to simmer and add chives. Drain ravioli and toss into pan with calamari. Toss to coat and mix gently. Pour into warm platter and serve immediately.