Stir tomatoes, balsamic vinegar, extra virgin olive oil, basil, cayenne pepper, salt, and black pepper together in a bowl. Let sit until flavors blend, at least 30 minutes.
Preheat an outdoor grill for medium-high heat and lightly oil the grate. Brush bread slices with olive oil.
Cook bread slices on the preheated grill until browned and crispy, 2 to 3 minutes per side.
Brush swordfish steaks with grapeseed oil and season with salt and black pepper.
Cook swordfish steaks on the preheated grill until fish flakes easily with a fork, about 4 minutes per side.
Divide bread slices between two plates and top each plate with 1 swordfish steak. Spoon 1/2 of the cherry tomato mixture over each steak.
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