In this paper, we propose a pole-placement technique for second-order, time-delayed systems that combines the strengths of the method of receptances and an optimization-based strategy. The method of receptances involves solving an algebraic system of equations to obtain the closed-loop gains that place the poles of the system at desired locations. The method of receptances is simple and efficient, but the placed poles may not be the rightmost poles so the resulting closed-loop system may not be stable. By contrast, an optimization-based approach can explicitly consider the rightmost pole in the objective function and thus can guarantee its location. In this work, we use Galerkin approximations to obtain the characteristic roots of time-delayed systems. When the method of receptances provides an unsatisfactory solution, we use particle swarm optimization to improve the location of the rightmost pole. The proposed approach is demonstrated with numerical studies and is validated experimentally using a 3D hovercraft apparatus. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.