Preheat an oven (or toaster oven if you have it) to 250-degrees. Dry your tilapia filets well with a paper towel to remove excess moisture.
Lightly coat the filets in flour on both sides. Season with salt and pepper.
In a pan over medium-high heat, melt the butter. When hot, add the tilapia, searing on each side for 2-3 minutes. When both sides are nicely browned, transfer to a 250-degree oven to continue cooking while you make the sauce.
Keeping the same pan over medium heat, add the chicken broth and scrape up the brown bits from the bottom of the pan with a spatula or wooden spoon. Add the quartered tomatoes and let simmer for 5 minutes. You’ll see the tomatoes starting to stew in the broth- this is a good thing!
Add the capers and balsamic vinegar, and let sauce cook for another 1-2 minutes.
Place tilapia on a plate, and serve topped with the tomato sauce. Enjoy!