The paper considers the problem ofH2optimal approximation of a high-order system by a low-order system with delay. An algorithm to solve this problem is presented. It consists of optimization with respect to the delay only where the rational part of the model and the quadratic cost are given by a solution of an equivalent order reduction problem without delay. It is shown by means of an example that introduction of delay into the model leads, in certain cases, to considerable improvement in the approximation. The results are extended to multiple-input multiple-output systems and also to frequency-weighted order reduction.