Sprinkle both sides of halibut with salt and pepper, then sprinkle top of fillets with 2 teaspoons dill; place fish on prepared steamer rack.
Combine sake and onion in large pot; bring to boil. Continue to boil 2 minutes.
Add carrots and garlic to pot; return to boil.
Place steamer rack with fish over liquid in pot. Cover pot tightly and steam fish until just opaque in center, about 8 minutes.
Transfer fish to platter.
Cut each fillet crosswise in half; cover with foil. Discard onion. Using slotted spoon, transfer carrots and garlic to small bowl; mix in butter and remaining 2 teaspoons dill. Season with salt and pepper. Spoon carrots alongside fish on platter. Boil liquid in pot until reduced to 6 tablespoons, about 3 minutes.