Structural vibrations often cause problems in high precision instruments, which may be solved by introducing passive damping. In this paper, different ways of introducing passive damping via viscoelastic materials (VEM) are discussed. Discrete damping elements and constrained layer (CL) configurations are selected and used to efficiently damp an open aluminum box. For the constrained layer configurations, a distinction is made between full and partial coverage of the structure. The steady-state dynamics of the box are simulated using a finite element (FE) model, which includes frequency dependent VEM properties. This model is used to find a design that possesses high damping while taking into account design constraints. The simulation results are experimentally validated using both modal parameters and frequency response functions (FRFs). For the computation of model based FRFs, a new method based on Interpolated Modal Parameter Superposition (IMPS) is proposed. Model based results and experimental results show good resemblance, even without updating the model with deviations in the realized structure. The local dampers add most damping to a limited number of modes. Partially covering the box with CL dampers is found to be more effective than full coverage of the structure with the same mass addition.