Prepare the tomatoes for stuffing as described in Step 1 of Tomatoes Stuffed with Shrimp.
Put tuna in a bowl and mash to a pulp with a fork.
Add mayonnaise, holding back 1 to 2 tbsp (15 to 30 ml), plus mustard and capers. Mix with the fork until uniform. Taste and correct for salt.
Shake off drained liquid from tomatoes without squeezing and stuff to the top. Spread the reserved mayonnaise over the tops, garnish with an olive slice, a strip of red or yellow pepper, a ring of tiny capers, or parsley leaves, and serve at room temperature or slightly chilled.