Compensation for mutual coupling in antenna arrays by matrix multiplication is compared to the use of dummy elements. A least squares estimation of the coupling matrix is made, including co- and cross-polar coupling. We show that compensation for measurements off the phase center is important as well as a proper assumption of the ideal element pattern. We study the performance of a dual polarized patch array with respect to far-field phase error, signal-to-interference reduction, and cross-polarization level. In all aspects, the performance of the compensation method exceeds or equals the use of dummy elements.