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Former antenna engineer here. I had a passing interest in knowing how safe I was in my work. Unfortunately, research in the field resulted in very much the kind of answers that are presented here. One researcher would present a paper saying, as long as you're not getting warm, your fine. Another would say were already all dead. Microwaves ARE harmful. It's a matter of degree. Tissue heating and damage to DNA were two modes of harm. There was a third I can't remember at the moment. I've never really understood why tissue heating was considered harmful if it wasn't, you know, burning you, but scientists seem to think so.
Bottom line is, I think more research is needed on the subject. Until then pretty much every country has rules about the power level that is safe for humans. I had to routinely calculate the minimum safe distance from a radiator for testing and installation purposes. They also have rules about the amount of power allowed to be radiated into ones head. This is called SAR (specific absorption rate). In the US it is the FCC that regulates these values. You can look them up there.
My advice, until someone can clearly provide a super accurate answer, I would err on the side of caution. Whenever I can, I use the speaker phone on my cell phone to keep it away from my head and when I get to where I'm going, I take it out of my pocket and keep it nearby, but not directly against my skin (power level drops significantly with distance). And I would NEVER voluntarily get warmed by a microwave device. But, if you have a liberal attitude toward your children being born with flippers, you do you.
Wait, DNA damage? With non-ionizing radiation? How?
Um, I probably have the research paper somewhere.
You would be more likely to destroy your sperm and become infertile before your children have flippers. (Which is an extremely unlikely thing to happen. The vast majority of us have a phone next to our bits at all times, even with all the plastic in us it hasn't detrimental affected our ability to procreate yet.)
Your cell phone isn't going to create enough power to do damage to yourself, unless the battery explodes.