This paper describes the optimisation of the eddy current damping, applied in a passive tuned mass damper (TMD). A semi-analytical model based on scalar potential formulation is extended for different permanent magnet (PM) topologies. Optimal design parameters are acquired by particle swarm optimisation. A 3-DoF mechanical model is presented to predict the quality reduction factor of the TMD. Measurements are performed for validating the semi-analytical model. Furthermore, an experiment is carried out to test a TMD with two optimal PM topologies for sinusoidal excitations.