Piaget Polo 8273 18K Quartz - Steve Martin - Planes, Trains and Automobiles
The watch gets a very good close-up early in the film. Later, Steve Martin's character trades the Piaget watch for a night in a hotel.
The Piaget has a gold case and black leather strap. It's possibly the reference number 8273 (with 27mm case) but a similar model is the 8673 (31mm).
Steve Martin's travel partner Del Griffith, played by John Candy, wears a Casio A159W.
With thanks to From Tailors With Love for spotting the watch