Close-binary central stars of planetary nebulae (CSPNe) provide an opportunity to explore the evolution of PNe, their shaping, and the evolution of binary systems undergoing a common-envelope phase. Here, we present the results of time-resolved photometry of the binary central stars (CSs) of the PNe NGC 6026 and NGC 6337 as well as time-resolved spectroscopy of the CS of NGC 6026. The results of a period analysis give an orbital period of 0.528086(4) days for NGC 6026 and a photometric period of 0.1734742(5) days for NGC 6337. In the case of NGC 6337, it appears that the photometric period reflects the orbital period and that the variability is the result of the irradiated hemisphere of a cool companion. The inclination of the thin PN ring is nearly face-on. Our modeled inclination range for the close central binary includes nearly face-on alignments and provides evidence for a direct binary-nebular shaping connection. For NGC 6026, however, the radial-velocity curve shows that the orbital period is twice the photometric period. In this case, the photometric variability is due to an ellipsoidal effect in which the CS nearly fills its Roche lobe and the companion is most likely a hot white dwarf. NGC 6026 then is the third PN with a confirmed central binary where the companion is compact. Based on the data and modeling using a Wilson-Devinney code, we discuss the physical parameters of the two systems and how they relate to the known sample of close-binary CSs, which comprise 15%-20% of all PNe.