Brush salmon fillets on both sides with roughly half the honey, then drizzle with roughly half the lime or lemon juice, then coat completely with flour.
Heat oil in a large pan over medium-high heat for 2 minutes until shimmering. Slide the salmon fillets into the pan and fry for 3-4 minutes on each side until golden brown. Increase heat to high, add a spoonful of the remaining honey to the pan to caramelize, then deglaze with the remaining lime or lemon juice.