Fill a small bowl with warm water and several drops of dish soap. Stir the solution until the water is sudsy.
Saturate an abrasive sponge with the solution and wring out the excess water. Scrub away surface dirt, dust and other residue from the top, bottom and sides of your luggage. Wipe the luggage dry with a microfiber cloth.
Apply a small amount of rubbing compound to a flannel cloth and spread it over the luggage shell. Buff the entire piece of luggage using the flannel cloth to restore its original shine. Repeat for each piece of luggage.
Load your luggage with care. If you are taking a trip by car, avoid stacking anything heavy or sharp-edged on top of your polycarbonate luggage.
Travel with your piece of polycarbonate luggage as a carry-on item if it fits your airline's size requirements. This allows you to avoid rough handling during luggage loading. If you must check your piece of luggage, place "Handle With Care" or "Fragile" tags in prominent locations.