Travel was relatively free of wrinkling when men could wear classic 15 ounce (or heavier) tweed like the green suit in the illustration. Unfortunately, tweed is too warm for the much of the year. And most of today's year-round worsteds wrinkle like crazy when sat upon, which means they don't travel well. But there's a twisted solution out there.
Most suit cloths, particularly the lighter worsteds, are woven of yarns combed flat, which means they will bend and stay bent. But when yarns are tightly twisted together before weaving, they bounce back into shape much more quickly, because each twist acts like a spring. The combination of twist yarns and a porous weave makes for cloth that wears cool and resists wrinkling.
Traditional fresco is perhaps the best known cloth that's made with twisted yarn. Fresco (a trademark of Hunt & Winterbotham), and its relations like CrispAire from Holland and Sherry, is made by twisting a double and a single yarn together, producing a thread that, when woven into cloth, retains its shape. Which is exactly what's required when a man faces one of those days that will begin with a flight that will be followed by a meeting that's followed in turn by another flight.
Though it's usually thought of as summer cloth, heavier weight fresco can do duty most of the year. A travelling man can be impeccable all day long with a half lined charcoal gray single breasted suit made from the 14 ounce version.