The ability to reconstruct high-momentum muon tracks in ATLAS with good momentum resolution is closely connected to a good understanding of the ATLAS tracking detectors alignment and of the related uncertainties. Moreover, an optimal selection of muon candidates with transverse momentum of the order of TeVs is a critical factor in the sensitivity of analyses looking for new high-mass resonances, such as Z' ->μμ and W' -> μν searches. This
contribution provides an overview of the method used in muon reconstruction to account for the differences in position and orientation of the various detector elements, between the geometry assumed in tracking and the real detector. Furthermore, the requirements that define the identification of high transverse momentum (pT) muons in the full Run~II ATLAS~dataset are detailed, together with several innovations. Such requirements have been tuned to select muons with the best possible momentum resolution, thus ensuring that candidates fulfilling the criteria are of the highest quality. The performance of the q/p criterion of the high-pT muon selection is also discussed, based on the result of measurements performed in data and simulation samples corresponding to an integrated luminosity of 139 fb-1.