A surgical microscope is a stereo, optical device that is positioned near the patient to magnify, illuminate and record the working area during surgery. The different types of surgical procedures, the variety of tools used by the surgeon and the varying viewpoint of the surgeon combined, makes it a very dynamic situation where the microscope should fit in. (Re)positioning the microscope on different locations and under different angles is therefore essential. The support system of the microscope should allow for manual, effortless and fluent repositioning to make it extremely user-friendly. Activation of the brakes in all the joints turns the flexible system into a rigid one. In this rigid mode the support system should be a steady base for the microscope, but certain support systems currently on the market cannot realize this. The microscope keeps vibrating in its eigenmode for too long after a perturbation from its equilibrium position, which causes a deteriorated image. A quicker return to the equilibrium position allows the surgeon to continue the operation without much delay. An investigation in the design of a steady but repositionable support system for a surgical microscope is therefore desired. The strategy used in this thesis to improve the design of the system is by creating a dynamic simulated model of the microscope support system in order to perform a free vibration analysis. The model has been validated with vibration measurements performed on an actual system. To investigate possible improvements of the vibration response, the model has been subjected to a set of parametric experiments. A second strategy to improve the vibration response is by implementing a subsystem with damping properties: A tuned mass damper. The results of the parametric experiments show that the settling time of the support system can be reduced with 17.5% by slight adjustments to certain design variables. These results have been transformed into design recommendations. The tuned mass damper has successfully been implemented in the simulated model of the support system. This subsystem has great damping properties: The addition of a tuned mass damper shows that the settling time can be reduced with 77.4%. When a tuned mass damper is implemented in the support system of a surgical microscope, delays after microscope repositioning actions will significantly be reduced which shortens the total operation time. Verification of these results in practice are left for future work.