A combination of analytical and numerical time-delay-system spectrum-shaping tools are applied to the design of the robust delayed resonator. First, the delayed resonator model is turned into a dimension-less form with the objective to generalize the derived results. The main theoretical result is then provided as a complete parameterization of the proposed resonator feedback with two delay terms to assign a pair of roots with multiplicity two on the imaginary axis. In the frequency-domain, the double roots are projected to widening the stop-band in the active absorber frequency response, which increases its robustness in vibration suppression. On the other hand, they have a destabilizing effect on the overall system dynamics. The stabilization is subsequently performed by an additional controller via spectral optimization. The design is thoroughly validated by both simulations and experiments where the results are compared with the classical delayed resonator.