Prepare a charcoal or gas grill for high heat (450 to 550; you can hold your hand 5 in. above cooking grate only 2 to 4 seconds). In a medium bowl, whisk together garlic, lemon juice, 1/2 cup oil, salt, and pepper.
Pour 1/4 cup dressing over sardines in another medium bowl and let sit 10 minutes.
Meanwhile, add beans, tomatoes, and parsley to remaining dressing and toss to coat.
Using a wad of oiled paper towels and tongs, oil cooking grate. Starting with skin side down, cook sardines, turning once, until cooked through and dark grill marks appear, about 5 minutes.
Divide bean salad among 4 plates. Top each with 2 sardine pieces.
