Heat the olive oil and butter in a large skillet over medium heat until the butter melts. Add the carrots and cook, turning from time to time, until tender and lightly golden, about 8 minutes.
Add the rosemary and cook for 1 to 2 minutes longer, stirring occasionally.
Swirl in the orange juice and water. Season with salt and pepper.
Reduce the heat to low, and let the carrots simmer, partially covered, until nearly all of the liquid has cooked off, about 10 minutes. Season with salt and pepper, if needed, and serve.