The $^{169}\mathrm{Tm}(n,2n)^{168}\mathrm{Tm}$ and $^{169}\mathrm{Tm}(n,3n)^{167}\mathrm{Tm}$ cross sections have been measured in the neutron energy range between 15 and 21 MeV using the $^{3}\mathrm{H}(d,n)^{4}\mathrm{He}$ neutron source reaction. The $^{169}\mathrm{Tm}(n,3n)^{167}\mathrm{Tm}$ data are intended to provide an accurate database for interpreting so-called reaction-in-flight neutron yields, which provide a sensitive tool for studying properties of the deuterium-tritium plasma created in inertial confinement fusion laser shots at the National Ignition Facility at Lawrence Livermore National Laboratory. The data are compared to previous data and evaluations for the reaction studied and are found to be in good agreement with the ENDF/B-VIII.0 evaluation, although small adjustments are necessary for the $^{169}\mathrm{Tm}(n,3n)^{167}\mathrm{Tm}$ reaction. For the first time in any $(n,2n)$ cross-section measurements to date, a comprehensive data set ranging from threshold to 21 MeV has been obtained by the same group.