In a small bowl, whisk together lime zest and juice, honey, balsamic, and olive oil together. Taste and add more honey or balsamic if needed. (Depending on how sweet your vinegar is, you may want more honey). Pour half of the glaze into a zip-top bag or airtight container. Add salmon to the bag or container. Marinate 10-45 minutes. Reserve remaining glaze.
Place salmon skin side down on a baking sheet lined with foil. Set an oven rack 5-6 inches from the heat. Broil salmon for 3 minutes. Brush the second half of the glaze over the salmon. Broil another 3-4 minutes. Check for doneness. Broil an additional 1-3 minutes as needed*.
*A rule of thumb for broiling salmon is about ten minutes of broiling for every inch of thickness of the fillet. Naturally, a thinner piece of fish will take less time. For a ½” fillet, broil the fish for 5-7 minutes, or so.