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In this paper we revisit the problem of identifying bona fide clusterCepheids by performing an all-sky search for Cepheids associated with openclusters and making use of state-of-the-art catalogued information for bothCepheids and clusters, based on the unparalleled astrometric precision of thesecond and early third data releases of the Gaia satellite. We determinemembership probabilities by following a Bayesian approach using spatial andkinematic information of the potential cluster-Cepheid pairs. We confirm 19Cepheid-cluster associations considered in previous studies as bona-fide, andquestion the established cluster membership of six other associations. Inaddition, we identify 138 cluster Cepheid candidates of potential interest,mostly in recently discovered open clusters. We report on at least two newclusters possibly hosting more than one Cepheid. Furthermore, we explore thefeasibility of using open clusters hosting Cepheids to empirically determinethe Cepheid period-age relation through the use of Gaia and 2MASS photometryand a semi-automated method to derive cluster ages. We conclude that the usageof cluster Cepheids as tentative probes of the period-age relations still facesdifficulties due to the sparsely populated red giant branch and thestochastically sampled main-sequence turn-off of the open clusters, making agedeterminations a challenging task. This biases the age-dateable clusterselection for Cepheid period-age studies towards older and high-mass clusters.

A revisited study of Cepheids in open clusters in the Gaia era