The mobile radio in the Apple Watch, at least according to Apple, does not work when you are outside of the region where the Watch was purchased. 4G works fine on the iPhone handset but the Watch won't independently connect to a local mobile network sans the iPhone.
(For example: I bought my Watch in the U.S. While on vacation to Ireland, my iPhone connected to Vodafone IE without a problem. But my Watch showed "no cellular service" if it was out of range of my iPhone and a wifi network.)
Is the watch's 4G free (no user plan required)? If so, that's probably why; they don't want to eat the unpredictable international costs. Free cellular on e-readers and other devices tends to work like this.
It's not provided by Apple, but rather your mobile carrier. They may or may not provide it for free. In the UK, it can cost as much as your current plan does just to enable your watch to share your plan.
(For example: I bought my Watch in the U.S. While on vacation to Ireland, my iPhone connected to Vodafone IE without a problem. But my Watch showed "no cellular service" if it was out of range of my iPhone and a wifi network.)