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To calculate local specific absorption rate (SAR) correctly, both the amplitude and phase of the signal in each transmit channel have to be known. In this work, we propose a method to derive a conservative upper bound for the local SAR, with a reasonable safety margin without knowledge of the transmit phases of the channels.The proposed method uses virtual observation points (VOPs). Correction factors are calculated for each set of VOPs that prevent underestimation of local SAR when the VOPs are applied with the correct amplitudes but fixed phases.The proposed method proved to be superior to the worst-case calculation based on the maximum eigenvalue of the VOPs. The mean overestimation for six coil setups could be reduced, whereas no underestimation of the maximum local SAR occurred. In the best investigated case, the overestimation could be reduced from a factor of 3.3 to a factor of 1.7.The upper bound for the local SAR calculated with the proposed method allows a fast estimation of the local SAR based on power measurements in the transmit channels and facilitates SAR monitoring in systems that do not have the capability to monitor transmit phases.