Heat the oil, olives, garlic and, capers in a large deep skillet over medium heat until garlic is lightly golden brown, about 2 minutes. Remove from heat and mix in broth and marinara sauce.
Add linguine and bring to a boil. Reduce heat and simmer, stirring often, for 10 minutes.
Nestle shrimp in mixture and cook until opaque throughout, 3 to 4 minutes. Fold in tomatoes, basil, and 1⁄2 teaspoon pepper.