Preheat oven to 375 degrees with rack in the center. Bring a large pot of water to a boil and add salt. Add the shells and cook, gently stirring occasionally, until just tender, according to package directions. Drain and rinse with cool water.
Meanwhile, combine ricotta with half of the mozzarella. Either spoon in the filling or transfer filling to a resealable plastic bag and press to seal. Then, using scissors, snip a corner of the bag so the opening is 1/2 inch wide.
To fill, hold a shell in your hand and squeeze gently to wide the opening. With your other hand, hold the bag, position the tip in the shell and squeeze gently to fill, taking care not to overfill. Set the shells on a work surface and repeat with remaining pasta and filling. Add any remaining cheese mixture to any less-filled shells, so they are all more or less evenly filled.
Spoon 3/4 cup of the sauce into each of 2 medium 1 1/2- to 2-quart glass or ceramic baking dishes. Arrange stuffed shells in the dishes, open side up, and top each dish with 1 1/2 cups sauce. Sprinkle Pecorino Romano and remaining mozzarella on top and cover with foil.
Bake for 30 minutes, then uncover and bake until lightly bubbling and browned in spots, 15 to 20 minutes. Let the shells sit for 15 minutes before serving.
