Place shrimp in a colander; rinse frequently with cold water until thawed, about 5 minutes. In a covered 5- to 6-quart nonstick pan over high heat, bring 2 1/2 to 3 quarts water to a boil.
Break off and discard tough stem ends from asparagus. Rinse asparagus and cut diagonally into 1 1/4-inch lengths.
Add linguine and shrimp to boiling water; cook, uncovered, until pasta is barely tender to bite and shrimp are opaque but still moist-looking in center of thickest part (cut to test), 2 to 3 minutes. Wash colander and pour pasta and shrimp into it; rinse with hot water and drain.
Rinse pan and return to high heat. When dry, add oil, garlic, and asparagus. Stir often until garlic begins to brown, about 2 minutes. Add tomatoes, cilantro, and 1/2 cup broth; bring to a boil, then reduce heat to medium.
Pour shrimp mixture into pan. Mix until pasta is hot, 1 to 2 minutes. For a moister dish, add 2 to 4 more tablespoons broth. Pour into a wide bowl. Add salt and pepper to taste.