The KM3NeT collaboration operates two Cherenkov neutrino telescopes in the deep Mediterranean sea, ORCA and ARCA. Both detectors consist of an array of light-sensitive detectors called Digital Optical Modules (DOMs) assembled along vertical strings anchored to the seafloor. Although the abundant muon flux from cosmic ray air showers is a background for the main scientific objectives of KM3NeT/ORCA and KM3NeT/ARCA, it can be exploited in various ways for calibration purposes. In this contribution, the methods implemented within the KM3NeT calibration workflow which exploit the muon track reconstruction are presented. For the latter, a likelihood fit of a track hypothesis to a set of observed hits on the DOMs is performed. For calibration purposes, the optimal position, time reference and orientation of each string of the detector can be found as the parameters maximizing the overall likelihood of reconstructed muon tracks. The muon track quality method is shown to reach the desired accuracy in time and position, allowing for the determination of the relative time offsets between strings. It also represents an important tool to cross-check position and orientation calibrations obtained by other means. Another muon-based calibration method is used to determine the relative time offsets between DOMs. It is based on the evaluation of the difference between the measured hit time and the one predicted from the fitted muon track’s position.