We have observed spectra from highly charged zinc ions in a variety of laser-produced plasmas. Spectral features that are Na - and Mg -like satellites to high- n Rydberg transitions in the Ne -like Zn XXI spectrum are analyzed and modeled. Identifications and analysis are made by comparison with highly accurate atomic structure calculations and steady state collisional-radiative models. Each observed Zn XX and Zn XIX feature comprises up to approximately 2 dozen individual transitions, these transitions are excited principally by dielectronic recombination through autoionizing levels in Na - and Mg -like Zn19+ and Zn18+. We find these satellites to be ubiquitous in laser-produced plasmas formed by lasers with pulse lengths that span four orders of magnitude, from 1 ps to approximately 10 ns. The diagnostic potential of these Rydberg satellite lines is demonstrated.