Upvote:1
I'd be careful, especially if the watches are valuable.
The US has a nasty process called "civil forfeiture" which is a fancy word for "TSA and local law enforcement can legally steal your stuff" and in some airports it's big business. In essence the TSA can tip of local law enforcement that you are carrying valuables. Police then confiscates your assets or cash simply be claiming it may be related to an illegal activity. No proof, evidence, or specific cause required.
While this is more likely to happen with cash and international travel, domestic cases and non-cash seizures are not unheard of either. See https://ij.org/wp-content/uploads/2020/07/Jetway-Robbery-July-2020-WEB-FINAL.pdf
Upvote:5
Not only you can, but you definitely should keep the watches in your carry-on so you can keep a close eye on them.
However, the cases may be an issue depending on their size, you need to make sure you don't exceed the carry-on allowances (number, size and/or weight) for your specific situation (depends on airline, class of service and possibly more parameters). If they do not fit, then you'll need to have those in your checked luggage, and use alternate means to protect the watches.
Be prepared for security to ask for inspection. If the watches are quite obviously valuable (e.g. yellow or rose gold, precious stones, or very recognisable brands) you can usually ask to move to a separate inspection area rather than opening it in front of everyone (though I can't quite remember if TSA in the US are agreeable to that — on the other hand I believe they are less prone to request visual inspection than in other places).