Sunset rainbows are special for few reasons. The sun's rays are nearly horizontal, so the top of the rainbow will be high in the sky. In fact, a sunset rainbow is the widest arc you'll ever see from the ground: almost half of the full-circle rainbow can become visible, and you'll need a wide angle lens to capture it all. This means the ends of the arc are nearly vertical as they intersect the horizon. Sometimes only the end segment of the rainbow appears, and if you see a photo such as ours of a vertical rainbow at the horizon, you'll know it was made at sunset (or sunrise).
At sunset, the sunlight contains more red hues and less blue (because of atmospheric scattering). This will affect the appearance of the rainbow by emphasizing the red bands and muting the blue bands. The same red tint will apply to anything on the ground illuminated by the sunset. The effect can be quite dramatic.
Be sure to turn around next time you're photographing a sunset, and see if the sky behind holds anything interesting.