The process $pp → pμ^{+} μ^{−}$ $p^{∗}$ has been observed at the LHC for dimuon masses larger than 110 GeV in $pp$ collisions at $\sqrt{s}$ = 13 TeV. Here $p^{(∗)}$ indicates the second proton is undetected, and either remains intact or dissociates into a low-mass state $p^{∗}$. The scattered proton has been measured in the CMS-TOTEM Precision Proton Spectrometer (CT-PPS). The spectrometer operated for the first time in 2016, collecting $∼10fb^{−1}$ of data in regular, high-luminosity fills. The procedure for detector alignment, optics corrections, and data analysis including background estimate are described. The present data constitute the first evidence of this process at such masses. They also demonstrate that CT-PPS performs as expected.