We investigated the occurrence of classical (type-I) Cepheid variable stars (henceforth Cepheids) in dynamically evolving star clusters from birth to an age of approximately 300 Myr. The clusters are modelled by the Aarseth code NBODY6, and they feature a realistic stellar initial mass function and initial binary star population, single star and binary star evolution, expulsion of the primordial gas, and tidal field of the galaxy. Our simulations provide the first detailed dynamical picture of how frequently Cepheids remain gravitationally bound to their birth clusters versus how frequently they occur in the field. They allow us to quantify the relevance of various cluster ejection mechanisms and how they depend on stellar mass. Overall, the simulations agree with the empirical picture that a small fraction (approximate to 10%) of Cepheids reside in clusters, that cluster halo membership is relatively common, and that the majority of Cepheid hosting clusters only have a single Cepheid member. Additionally, the simulations predict that (a) Cepheid progenitors are much more likely to escape from low-mass than higher mass clusters; (b) higher-mass (long-period) Cepheids are approximate to 30% more likely to be found in clusters than low-mass (short-period) Cepheids; (c) the clustered Cepheid fraction increases with galactocentric radius since cluster dispersal is less efficient at greater radii; (d) a lower metallicity reduces the overall clustered Cepheid fraction because the lower minimum mass of Cepheids leaves more time for cluster dispersal (this primarily affects short-period Cepheids); and (e) high-mass clusters are much more likely to have more than one Cepheid member at any given time, in particular at a lower metallicity. We interpret the results as outcomes of various aspects of star cluster dynamics. The comparison of predicted and observed clustered Cepheid fractions, f(CC), highlights the need for additional cluster disruption mechanisms, most likely encounters with giant molecular clouds, to explain the observed fractions.