As shown in Grabowski (1983), the problem of evaluation of the quadratic performance index for delay-differential systems of neutral type can be effectively solved by the use of Lyapunov functionals. In this paper another solution to that problem, based on the frequency-domain approach, is proposed. With the use of Plancherel's theorem and other tools of complex analysis, this task is reduced to a Riemann-Hilbert problem, an explicit solution to which is found by elementary methods. Our results can be regarded as a generalization of those due to Walton and Marshall (1984, 1987). Two simple examples of application are also provided.