This paper introduces a rigorous and fast procedure for accurate assessment of the peak averaged specific absorption rate (SAR), quantifying the user exposure to the electromagnetic field radiation from new-radio communication devices. Focus is lent to the specific class of user equipment that exploit multiple-input multiple-output (MIMO) technology and using exclusive simultaneous excitations of the active antenna-array system, such as expected on 5G devices. In contrast with the required N(N-1)+1 measurements on traditional SAR systems that only take measurements of the amplitude of the electric field, it is demonstrated in this paper that only N+1 number of measurements are required to evaluate the true SAR of a Nantenna MIMO thanks to using a vector near-field based SAR measurement system.