This article presents a three-degree-of-freedom (DoF) magnetically levitated vibration compensating measurement platform (MP) with arbitrary operation orientation for robot-based surface inspection of free-forms. The MP design comprises an internal position sensor system, which is used in feedback control to maintain a free-floating position in six DoFs with respect to its supporting frame when approaching a sample (stabilization mode). In addition, the integrated design includes three tracking sensors measuring the out-of-plane position of the MP to a sample surface. The entire system can be mounted as an end-effector of an industrial robot with the MP carrying a desired measurement tool. Disturbing environmental vibrations are actively compensated by maintaining a constant position of the MP with respect to a sample surface (tracking mode). The control design includes single-input single-output position controllers for all DoFs, achieving a bandwidth of about 130 Hz. By means of a cross-fading error gain, an efficient control transition between stabilization and tracking mode is enabled. A vibrating target is used to evaluate the vibration compensation performance of the tracking module for standardized floor vibration profiles. Attenuation between 35 and 20 dB for out-of-plane vibrations below 40 Hz is achieved. In the time domain, vibration profiles with 15.7 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m rms and 95 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> rad rms are reduced to 1.6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m rms and 21 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> rad rms, respectively.