A phone's specific absorption rate (SAR) reveals the maximum amount of radiation the human body absorbs from the phone while it's transmitting. SAR testing ensures that the devices sold in the U.S. comply with the Federal Communications Commission (FCC) SAR exposure limit, but the single, worst-case value obtained from this SAR testing is not necessarily representative of the absorption during actual use, and therefore it is not recommended for comparisons among phones. In short, selecting a lower SAR phone will not reliably ensure lower radiation absorption during use. The FCC has more information at Specific Absorption Rate (SAR) For Cell Phones: What It Means For You.
"Possibly carcinogenic" was a phrase that may media outlets pulled out of the release, but it's a dangerous takeaway for consumers, out of context. "Possibly carcinogenic to humans", or group 2B, is a sub-classification or monograph, applied to agents by the IARC. Other agents (or items of everyday life) in Group 2B include pickled vegetables, lead and Potassium bromate — an oxidising additive common in flour. In all, there are 272 agents listed as possibly carcinogenic.
Let’s say you are in class, or at the movies, and you don’t want your phone to ring. Slip it into the fully shielded slot. In this position, RF signals in or out will be reduced almost to zero, which is enough to stop the phone from ringing in most circumstances unless you have an especially good connection. You can also store chipped cards (like credit cards) in here to prevent unintentional reading.

But the pair of studies by the US National Toxicology Program found “clear evidence” that exposure to radiation caused heart tumors in male rats, and found “some evidence” that it caused tumors in the brains of male rats. (Both are positive results; the NTP uses the labels “clear evidence,” “some evidence,” “equivocal evidence” and “no evidence” when making conclusions.)
While an increased risk of brain tumours from the use of mobile phones is not established, the increasing use of mobile phones and the lack of data for mobile phone use over time periods longer than 15 years warrant further research of mobile phone use and brain cancer risk. In particular, with the recent popularity of mobile phone use among younger people, potentially longer lifetime of exposure, WHO has promoted further research on this group and is currently assessing the health impact of RF fields on all studied endpoints. A cohort study in Denmark linked billing information from more than 358,000 cell phone subscribers with brain tumour incidence data from the Danish Cancer Registry. The analyses found no association between cell phone use and the incidence of glioma, meningioma, or acoustic neuroma, even among people who had been cell phone subscribers for 13 or more years. (4)
The energy of electromagnetic radiation is determined by its frequency; ionizing radiation is high frequency, and therefore high energy, whereas non-ionizing radiation is low frequency, and therefore low energy. The NCI fact sheet Electromagnetic Fields and Cancer lists sources of radiofrequency radiation. More information about ionizing radiation can be found on the Radiation page.