Heat a large cast iron skillet over medium heat. Add the almonds to the skillet, and cook them for 2-3 minutes- stirring and toasting them as they go. Transfer the toasted nuts to a separate dish, and set aside.
Pat the salmon dry between layers of paper towels. Let it rest and pat it dry again, because wet salmon will not sear. Season each filet with salt, pepper, & lemon zest. Rub it in to ensure a good seasoning.
Return the cast iron skillet to medium high heat, add the butter and let it melt but NOT brown.
Carefully add 2 filets to the pan, working in batches. Cook the salmon for 4 minutes per 1/2 inch thickness, without disturbing. Salmon cooks from the bottom up, when the salmon has gone from pale pink to white 3/4's of the way through- it's ready to be flipped.
Using a thin metal fish spatula, gently release the fish from the pan and flip it. Cook the fish for an additional minute. Remove the fish from the skillet, and place it in an oven safe dish. Keep it warm in the oven while you cook the remaining fish.
When the fish is done, slowly pour the amaretto into the pan. Add in the cherries and lemon juice, stirring well to incorporate. Let the mixture simmer for about two minutes, squishing the cherries with the back of a spoon to release the juices.
Serve the salmon, as is, with the cherry almond sauce spooned generously overtop. A bed of white rice makes a great side to this dish, rounding it out.