Gently pat the salmon dry and place in a deep container. If you start with frozen fillets, lay them on dry towels for a few minutes to absorb and excess moisture from freezing.

Crack some salt and pepper on both sides.

Squeeze the juice from the limes using a citrus press. They are really easy to use and all the seeds stay in the cup. Give the limes a hard roll on the counter to soften the inside and make it easier to get all the juices out. Press them right into a small sauce pan. Turn heat on to low. 

Add two or three whole sprigs of mint. Any kind of mint works, but I used peppermint. I like the flavor of it best. Let it simmer in the juice for about 5 minutes. Don't turn it up too high or it will evaporate!

Next, drizzle the honey into the pan. When it is totally dissolved, add the butter and the rum. Now just simmer until it starts to thicken. Cooking will remove the alcohol from the sauce.

Once the sauce is thickened and the flavors are all well blended, pour it over the salmon. Lay it skin side up first.

Let it sit for about 10 minutes, then turn it and leave it another 5 minutes. Meanwhile - start that grill!

Lay the salmon skin side down first. Baste the fish with the sauce and put the lid down, but don't leave! Stick around to make sure there is no flare up of the sauce.

Give it about five minutes, baste it again, then carefully flip it. The skin will likely stick to the grill, just scrape it off. If it stays on the salmon, great - especially if it's crisp! Again, cook for about five minutes then gently turn it again.

Baste a little more sauce on the top and check for doneness. Depending on how thick the salmon is, cooking time will vary. Give it a push on the top in the middle. You can feel the firmness. It should be firm but still have a little give. If it's a little pink in the middle, it's fine (better than sushi!). In any case, give it about 1 or 2 minutes more with the lid down to caramelize the glaze.

Remove from the grill and serve it with just a little more sauce on the top. It is wonderful!

Put the remaining sauce back into the sauce pan and bring to a boil. (This is a good time to make the salad). Stirring often, heat for about 3 to 5 minutes to thicken. Spoon over the fish.