Dry clean the jacket prior to traveling to remove any wrinkles. The jacket will come back slightly starched, which makes it easier to manage for folding. Professional cleaning also removes any stains or smells that you might not have noticed.
Open the jacket and lay it on a flat surface. The inside will be facing downward, while the sleeves and back will be facing upward. Adjust the jacket so it is smooth and free from wrinkles. Pull the collar straight and up. In this way, you will be folding the jacket inside out, which prevents external wrinkles.
Fold the sleeves of the jacket upward. The cuff will be even with the armholes of each sleeve. Adjust the folded sleeves, smoothing out wrinkles with your hands.
Fold the left side of the jacket backwards, over the folded sleeve, until the bottom hem of the jacket is even with the rear tail seam. Repeat with the right side.
Pack the sports coat into a structured carry-on -- that is, one with rigid sides -- by folding the coat in half horizontally, over the sleeves. The collar will be even with the back hem line. A rigid bag prevents contents from shifting or being squished by other on-board luggage.
If you must use an unstructured carry-on, such as a duffel bag, begin by folding the jacket vertically. Fold the coat over the sleeves so the two side hems are even with each other.