  The CMS detector at the LHC has recorded events from proton-proton
collisions, with muon momenta reaching up to 1.8 TeV in the collected dimuon
samples. These high-momentum muons allow direct access to new regimes in
physics beyond the standard model. Because the physics and reconstruction of
these muons are different from those of their lower-momentum counterparts, this
paper presents for the first time dedicated studies of efficiencies, momentum
assignment, resolution, scale, and showering of very high momentum muons
produced at the LHC. These studies are performed using the 2016 and 2017 data
sets of proton-proton collisions at $\sqrt{s} =$ 13 TeV with integrated
luminosities of 36.3 and 42.1 fb$^{-1}$, respectively.
