Regular battery-powered watches (and all other battery-powered tech, for that matter) also produce some level of EMFs, but that level is far lower than the amount emitted by tech devices that are plugged in, or that receive and transmit information wirelessly. The same rule applies however; if you can turn it off and keep it away from your body, then do so whenever possible.
Dr Devra Davis is an internationally recognised expert on electromagnetic radiation from mobile phones and other wireless transmitting devices. She is currently the Visiting Professor of Medicine at the Hebrew University Hadassah Medical School, and Visiting Professor of Medicine at Ondokuz Mayis University, Turkey. Dr Davis was Founding Director of the Center for Environmental Oncology at The University of Pittsburgh Cancer Institute —­ the first institute of its kind in the world, to examine the environmental factors that contribute to the majority of cases of cancer.
In conclusion: It is still unclear whether use of cellular technology is associated with an increased risk to develop malignant and benign tumors, but taking into account the results of recent studies, the Ministry of Health adopts the precautionary principle and follows the recommendations listed in the “Ministry of Health Recommendations” (below).
SafeSleeve is garbage. And the customer service is even worse. I bought one in October 2017 and by the end of January 2018 the sticky patch had worn off to completely no longer be able to hold my phone. I contacted the company, and they would not replace it even though they recognized it was due to “normal wear” because they only have a 60 day warranty. And offered only a one-time 25% off coupon. for a $45 case only to be guaranteed for 2 months is absurd to me! I asked to be contacted by a manager as they do not have a phone number listed anywhere, just email address and has been a week and no response. Totally ignored.

Although common sense, spending as little time on your computer as possible, and when you’re not using it, disabling the Wi-Fi connection or even turning your computer off completely, is recommended to help keep EMF pollution to a minimum. These devices emit a constant stream of EMFs when plugged in and “synced” up to a router or other wireless device.
Most of the research is attributed to "SPSU," which is presumably St. Petersburg State Polytechnic University, and some of the research, it is suggested, was conducted at the Kirov Military Medical Academy, though it's unclear why a military academy would conduct clinical research on civilian cell phone radiation. The names of the scientists who conducted these studies are conspicuously absent, as are any published results.
The frequency of radiofrequency electromagnetic radiation ranges from 30 kilohertz (30 kHz, or 30,000 Hz) to 300 gigahertz (300 GHz, or 300 billion Hz). Electromagnetic fields in the radiofrequency range are used for telecommunications applications, including cell phones, televisions, and radio transmissions. The human body absorbs energy from devices that emit radiofrequency electromagnetic radiation. The dose of the absorbed energy is estimated using a measure called the specific absorption rate (SAR), which is expressed in watts per kilogram of body weight.