PurposeMulti‐transmit MRI systems are typically equipped with dedicated hardware to sample the reflected/lost power in the transmit channels. After extensive calibration, the amplitude and phase of the signal at the feed of each array element can be accurately determined. However, determining the phase is more difficult and monitoring errors can lead to a hazardous peak local specific absorption rate (pSAR10g) underestimation. For this purpose, methods were published for online maximum potential pSAR10g estimation without relying on phase monitoring, but these methods produce considerable overestimation. We present a trigonometric maximization method to determine the actual worst‐case pSAR10g without any overestimation.Theory and MethodThe proposed method takes advantage of the sinusoidal relation between the SAR10g in each voxel and the phases of input signals, to return the maximum achievable SAR10g in a few iterations. The method is applied to determine the worst‐case pSAR10g for three multi‐transmit array configurations at 7T: (1) body array with eight fractionated dipoles; (2) head array with eight fractionated dipoles; (3) head array with eight rectangular loops. The obtained worst‐case pSAR10g values are compared with the pSAR10g values determined with a commonly used method and with a more efficient method based on reference‐phases.ResultsFor each voxel, the maximum achievable SAR10g is determined in less than 0.1 ms. Compared to the reference‐phases‐based method, the proposed method reduces the mean overestimation of the actual pSAR10g up to 52%, while never underestimating the true pSAR10g.ConclusionThe proposed method can widely improve the performance of parallel transmission MRI systems without phase monitoring.