Melt the butter in a large skillet over medium-high heat. Add the coriander seeds and toast 30 seconds. Add the carrots, then stir in the orange and lime juice, brown sugar, 1/4 cup water, 1/2 teaspoon salt, and pepper to taste. Bring to a boil, then cover and reduce the heat to medium low. Simmer, stirring occasionally, until the carrots are almost tender, 13 to 15 minutes.
Uncover, increase the heat to medium high and cook, stirring, until the liquid is reduced, 8 to 10 minutes. Transfer to a platter and sprinkle with the cilantro.