The underlying event in a proton-proton collision consists of multiple-parton interactions and beam remnants, which typically involve low energy scales. The modeling of these aspects of a collision is not always calculable in perturbative quantum chromodynamics, and is governed by phenomenological parameters that need to be "tuned" to observed data. The results of such an underlying-event tuning performed by the CMS experiment for the Pythia 8 and Herwig 7 generators are presented. Various assumptions in the proton parton distribution functions and parton shower development are tested. The derived tunes are validated using data of a wide range of physics processes, and provide a good description of CMS data at a center-of-mass energy $\sqrt{s} = 13$ TeV.