Combine beer, sugar, mustard, vinegar, caraway seeds and liquid red-pepper seasoning in large skillet. Bring to boiling.
Score top of kielbasa at 1-inch intervals. Add to skillet; simmer over low heat for 10 minutes.
Grill or broil kielbasa 3 inches from heat for 4 minutes, turning halfway during cooking and basting once or twice with beer mixture. Serve extra beer liquid on side, and steamed parsleyed potatoes with cherry tomatoes.