In a 1 1/2- to 2-quart heavy saucepan bring water, broth, rice, caraway seeds, and salt to a boil and cook, covered, over very low heat until liquid is absorbed and rice is tender, about 20 minutes.
Preheat broiler and butter a baking sheet.
Fluff rice with a fork. Fill a 1/3-cup measure with rice, packing it, and turn out onto baking sheet. Make 5 more rice cakes in same manner and arrange on baking sheet about 3 inches apart. Gently flatten cakes with back of a fork to 4 inches in diameter and cool 5 minutes. Brush rice cakes with butter and broil 3 to 4 inches from heat until pale golden, about 4 minutes.
