Add the oil and 1 tablespoon of the butter to a nonstick skillet and place over medium-high heat. Season the salmon on both sides with salt and pepper. Add the fish to the skillet and cook for 3 to 4 minutes per side, depending on the thickness of the fish and the degree of doneness you like. Remove from the skillet and keep warm.
Return the skillet to medium heat and add the honey, soy, remaining 2 tablespoons butter and half of the lime zest and juice. Cook, stirring, until the butter melts and starts to bubble. Cook for a minute until the sauce thickens a little. Add the salmon and spoon over the sauce. Cook for another minute, basting as you go. Sprinkle generously with the cilantro.
Stir the remaining lime juice and zest into the cooked rice. Serve the salmon with the rice, extra sauce and lime wedges on the side.