Drain the capers if packed in vinegar; soak, rinse, and drain if packed in salt.
Chop them fine.
Turn the oven on to 400.
Remove the salmon's skin, any loose membranes, and carefully pick out all bones.
Cut the fish into very small diced pieces and put in a bowl together with 2 1/2 tablespoons of olive oil, the chopped parsley, garlic, capers, 1 tablespoon of bread crumbs, salt and several grindings of black pepper.
Wash the tomatoes, cut them horizontally in half, and scoop out all the seeds and the centers to make a cup-like hollow.
Pat the inside of the tomatoes with a paper towel to soak up excess juice, then stuff them with the salmon mixture, pressing it down lightly as you do so.
There should be enough to form a mound.
Sprinkle the tops with the remaining bread crumbs and drizzle with remaining olive oil, holding back a few drops of the olive oil to grease the bottom of a baking pan.
Place the tomatoes on the baking pan and bake in the upper level of the preheated oven for 30-35 minutes or until the salmon stuffing has formed a light golden crust.