"Fine watchmaking" might bring to mind old, bespectacled men fussing with tiny gears in a dusty workshop. Fact: While fine watchmaking does have a rich history, it's anything but outdated. Modern craftsmen are in lockstep with avant-garde fashion designers, pushing boundaries to create fresh proportions, new materials, and never-before-seen functionality—yes, quite a bit like the edgiest looks from the runway. (And, in some cases, watches mimic their ready-to-wear big siblings with eye-watering haute couture pricing, too.)