In this paper, we develop an K-order model expressing the specific absorption rate (SAR) at an observation point when evaluating the electromagnetic exposure to multiple-antenna transmitters. By using the proposed model, we will be able to precisely estimate the SARs for different combinations of the relative phases of the sources, and thus to identify the maximum SAR. Detailed discussions on the K-order model and the estimation technique will be presented. We also conduct several measurements to verify the performance of the proposed estimation technique, and compare the effectiveness the proposed technique with conventional techniques. As a result, it is confirmed that the proposed technique with K-order estimations can considerably reduce the estimation errors, and thus giving highly precise estimated SAR values. In particular, when evaluating of the SAR of a three-antenna configuration, the maximum estimation error caused by conventional estimations is about 6%, which can be reduced to about 3% or 2% by the 1- and 2-order estimations, respectively.