This article presents a Harmonic Balance Method-based numerical strategy to provide a qualitative numerical characterization of a compressor blade’s dynamics when structural contacts occur with the surrounding casing. The mitigation of the Gibbs phenomenon follows a two-pronged approach: (1) a regularization of the unilateral contact law and (2) the adjustment of the Fourier coefficients by means of a Lanczos filtering technique. In order to validate the proposed approach, it is first applied to an academic cantilever rod undergoing unilateral contact constraints. An in-depth comparative analysis of the obtained results—with an emphasis on displacements, contact forces and velocities—with respect to a time integration-based reference numerical strategy underlines the relevance and accuracy of the proposed methodology. The latter is then applied to the vibration analysis of an industrial compressor blade: NASA rotor 37. For a given contact configuration, obtained results are thoroughly compared to those obtained with a previously published time integration-based numerical strategy with a distinct contact treatment algorithm. Particular attention is paid to demonstrate the accuracy of the methodology for the prediction of displacements, contact forces, velocities as well as stress fields within the blade. Notably, it is evidenced that the proposed methodology, contrary to the reference time integration-based numerical strategy, is able to capture the exact location of the blade’s nonlinear resonance.