I have an extensive watch collection. I typically don't travel with any of my very high-end watches in tow.
I have a few $200 to $500 watches that I typically wear on business and pleasure while traveling. My favorite traveling watch is actually a Croton Titanium that I purchased many years ago for about $200. Being Titanium, it's ultra-light, stylish, and unique. The few times I wore it through the MD, it did not set off the alarm. It's quartz movement so I never have to worry about it keeping time or being wound for the 3 years that the battery usually lasts. Best investment I ever made.
I leave the high-end watches in my collection at home, in my collection. Not worth damaging or losing them when I travel, as my schedule can be hectic.
Regardless of the watch;
I typically put them in my carry-on through the X-Ray. I rarely leave them on. When I leave my hotel or Home, I already have my jewelry in my carry-on. Once through Security, then I finish "Dressing".