In a large pot boil salted water and cook the rice until the grains are cooked, around 20 minutes. When done drain and add unsalted butter. Mix well
Preheat the broiler. Brush the fillets on both sides with the olive oil. Sprinkle with ¼ teaspoon of the salt. Arrange on a cookie sheet.
Melt the butter in a large skillet. When it is hot, add the tomatoes and sauté over medium high heat for about 1 minute to warm them. Add the remaining ¼ teaspoon salt, the pepper and the basil and set aside.
Meanwhile place the fillets under the broiler, about 2 inches from the heat source and cook for 2 minutes. Do not turn the salmon.
Arrange a nice scoop of rice in the middle of a plate. Spoon some of the tomatoes sauce over it. Place the salmon fillet over the rice-sauce. Spoon more tomato sauce over the salmon and serve immediately.