We analyse all potential combinations of Galactic Cepheids and open clusters (OCs) in the most up-to-date catalogues available. Isochrone fitting and proper-motion calculation are applied to all potential OC–Cepheid combinations. Five selection criteria are used to select possible OC Cepheids: (i) the Cepheid of interest must be located within 60 arcmin of the OC's centre; (ii) the Cepheid's proper motion is located within the 1σ distribution of that of its host OC; (iii) the Cepheid is located in the instability strip of its postulated host OC; (iv) the Cepheid and OC distance moduli should differ by less than 1 mag; and (v) the Cepheid and OC ages (and, where available, their metallicities) should be comparable: Δlog (t yr−1) < 0.3. 19 possible OC Cepheids are found based on our near-infrared (NIR) analysis; eight additional OC–Cepheid associations may be genuine pairs for which we lack NIR data. Six of the Cepheids analysed at NIR wavelengths are new, high-probability OC Cepheids, since they lie on the NIR period (P)–luminosity relation (PLR). These objects include TY Sct and CN Sct in Dolidze 34, XX Sgr in Dolidze 52, CK Sct in NGC 6683, VY Car in ASCC 61 and U Car in Feinstein 1. Two additional new OC Cepheids lack NIR data: V0520 Cyg in NGC 6991 and CS Mon in Juchert 18. The NIR PLR for our confirmed sample of OC Cepheids is MJ = (−3.12 ± 0.29)log (Pd−1) − (2.17 ± 0.29) mag, which is in good agreement with the best NIR PLR available for all Galactic Cepheids.