In this paper, we present a fast technique for estimating the specific absorption rate (SAR) of multiple-antenna transmitting devices such as mobile phones, which utilize two or more antennas in communication. SAR values for arbitrary relative phase combinations of the antennas at an observation point can be estimated from SAR measurements for several known relative phases at the same observation point. Several numerical and experimental validations on different antenna configurations and operating frequencies have been carried out to verify the proposed estimation method. It has been highlighted that the proposed estimation method is simple yet provides highly accurate estimated SAR values.