Reduced order models (ROMs) of turbine bladed disks (blisks) are essential to quickly yet accurately characterize vibration characteristics and effectively design for high cycle fatigue. Modeling blisks with contacting shrouds at adjacent blades is especially challenging due to friction damping and localized nonlinearities at the contact interfaces which can lead to complex stick–slip behavior. While well-known techniques such as the harmonic balance method (HBM) and Craig–Bampton component mode synthesis (CB-CMS) have generally been employed to generate ROMs in the past, they do not reduce degrees-of-freedom (DoFs) at the interfaces themselves. In this paper, we propose a novel method to obtain a set of reduction basis functions for the contact interface DoFs as well as the remaining DoFs called “adaptive microslip projection” (AMP). The method is based on analyzing a set of linear systems with specifically chosen boundary conditions on the contact interface. Simulated responses of full order baseline models and the novel ROMs under various conditions are studied. Results obtained from the ROMs compare very favorably with the baseline model. This study addresses the case of a shrouded blisk in microslip close to stick. The AMP procedure may be possibly applied to other systems with Coulomb friction contacts, but its accuracy and effectiveness will need to be evaluated separately.