We present a new numerical procedure for the robust stabilization of linear delay differential equations, based on the position of the eigenvalues in the complex plane. We assume static perturbations on the system matrices and express the robustness of the stability in terms of complex stability radii. In the numerical procedure, these stability radii are maximized as a function of the controller parameters. This corresponds to a H-infinity synthesis problem, which is solved by a quasi-continuous shaping of some frequency response plots. The structure of the algorithm is analogous to the continuous pole placement algorithm for the (non-robust) stabilization of linear delay differential equations.