watchintime i looked into this a good bit before travelling to Norway with stops to & from at Dulles and Brussels. What I went with was 2 watches on straps, put in a watch roll in my carry-on. Since i *really* like to know the time at a glance I also wore a plastic Garmin GPS watch through security. Once on the other side (total of 3 times) we stopped at an empty gate & swapped out for the Omega or Breitling to wear the rest of the way.
If you're bringing a Rolex on a bracelet (that will be me next trip) you can bring a watch box in your carry-on & still swap out on the way to the gate.
Main thing is to keep peoples eyes off your expensive watch *at* the TSA line; if you're extra cautious then don't be messing with the watch at your departure gate or on the plane either.
Read *many* mixed reports about whether TSA or EU security will let you continue to wear a mens steel watch through the scanners. They did let me wife wear her DateJust, never heard a single peep about any woman's watch or jewelry from security.
My last choice - by far - was gamble whether TSA wanted me to put my Globemaster in plastic dog-food bowl.