RV Tau variable stars are pulsating post-asymptotic giant branch stars identified by minima of alternating depth in their light curves, with formal pulsation periods on the order of 30-150 days. Some RV Tau variables exhibit additional, longer periodic variations in their average brightness, thought to be due to their large circumbinary disks partially obscuring the binary system. Vega et al. 2020 reported the first detection of X-rays from such an RV Tau variable star, U Mon, with the XMM-Newton X-ray Observatory. The origin of the X-ray emission from U Mon is unclear, but suggests that binary and/or circumbinary disk interactions may play a role. To determine if X-ray emission from these stars is common, we have performed a search for serendipitous observations of RV Tau variables with the Chandra and XMM-Newton X-ray Observatories. Of the 210 RV Tau variable stars considered, only 39 were observed by either mission. Based on our search, we detected clear evidence for X-ray emission from the RV Tau variable star HD 145532 and possible or spurious emission from several other RV Tau variable stars. Most of the serendipitously observed stars reside in the Galactic Bulge or the Large Magellanic Cloud, where detection is difficult because of crowding, intervening absorption, and distance. Targeted observations of more stars are needed to determine if X-ray emission from RV Tau variable stars is common. X-ray emission from this class of stars can provide important insight into processes in evolved binary systems. This project was supported in part by the NSF REU grant AST-1757321 and by the Nantucket Maria Mitchell Association.