There is, of course, antithetical research. But some of this was partly funded by cellphone companies or trade groups.

One example is the international Interphone study, which was published in 2010 and did not find strong links between mobile phones and an increased risk of brain tumors. The Centers for Disease Control and Prevention concluded in 2014 that “more research is needed before we know if using cell phones causes health effects.”

Another study, in The BMJ, which measured cellphone subscription data rather than actual use, said there was no proof of increased cancer. Yet even here, the Danish team behind the report acknowledged that a “small to moderate increase” in cancer risk among heavy cellphone users could not be ruled out.

But what does all this research tell the Apple faithful who want to rush out and buy an Apple Watch, or the Google and Windows fanatics who are eager to own an alternative smartwatch?

Dr. Joseph Mercola, a physician who focuses on alternative medicine and has written extensively about the potential harmful effects of cellphones on the human body, said that as long as a wearable does not have a 3G connection built into it, the harmful effects are minimal, if any.

“The radiation really comes from the 3G connection on a cellphone, so devices like the Jawbone Up and Apple Watch should be O.K.,” Dr. Mercola said in a phone interview. “But if you’re buying a watch with a cellular chip built in, then you’ve got a cellphone attached to your wrist.” And that, he said, is a bad idea.