Melt butter in heavy skillet over medium-high heat (NOT non-stick). Make sure the pan is nice and hot before adding the butter (it helps the scallops not to stick).
Sprinkle scallops with salt and pepper.
Add scallops to skillet and sauté until golden and just opaque in center, about 3 minutes per side.
Using tongs, transfer scallops to plates.
Add clam juice, lemon juice, mint, and chives to same skillet. You can also throw in a little dry white wine. Boil until sauce thickens enough to coat a spoon, about 3 minutes.
Pour the sauce over scallops and serve.
Steamed veggies, asparagus or broccoli is excellent with this.