The large number of star clusters in nearby galaxies permits us to statistically test the predictions of stellar, dust, and gas models. Using Hubble Space Telescope (HST) broadband plus Hα imaging combined with JWST near-infrared imaging, we use a total of 10 filters spanning near-ultraviolet through near-infrared wavelengths to model key physical parameters, including age, mass, and reddening, of 6130 star clusters in 16 nearby spiral galaxies from the Physics at High Angular resolution in Nearby GalaxieS sample, focusing on their ages, masses, and reddenings. We find that HST/Hα and JWST/NIRCam 2–3.6 μm photometry significantly improves our ability to disentangle the age–reddening degeneracy between young, gas- and dust-rich clusters and older, dustless clusters. The near-infrared data provide strong constraints on hot continuum dust and small polycyclic aromatic hydrocarbon emission for populations where gas and dust are present. These hot dust constraints demonstrate that Bruzual & Charlot stellar population models do not align with the observed near-ultraviolet-optical-near-infrared spectral energy distributions of star clusters in the first 10 Myr. We note that for old and low-metallicity globular clusters, the inclusion of narrowband Hα and/or broadband near-infrared data does not improve the determination of age and reddening parameters, due to the lack of stars capable of heating dust in the near-infrared regime.