We present observations and analysis of three barred S0 galaxies which contain smooth, luminous, stellar nuclear rings within their bars. These rings, which have little or no dust and are approximately the same color as surrounding bar and bulge, are probably the old remnants of bar-driven circumnuclear starburst episodes similar to those seen in many barred galaxies today. Using kinematic data from long-slit spectroscopy, we construct rotation and resonance curves and relate the relative sizes of the rings to possible bar resonances. Two of the galaxies are actually double-barred, with misaligned secondary bars inside the nuclear rings. In at least one of these (NGC 4340), the resonance curves indicate that the nuclear ring lies near or at one of the outer bar's inner Lindblad resonances; this is a plausible location for the secondary bar's corotation radius. We also discuss the difficulties inherent in detecting and identifying such rings, and show some of the surprising ways in which stellar rings can distort galaxy isophotes and ellipse fits.