We derive the second and most stringent limit to date of the X-ray/radio flux ratio (F_x/F_R) for the radio bursts associated with the recently identified source class, the Rotating Radio Transients (RRATs). We analyze 20.1 hr of rxte/PCA observations of RRAT J1819-1458 -- a period during which 350ppm23 RRAT radio bursts occurred, based on the previously observed average radio burst rate. No X-ray bursts were detected, implying an upper-limit on the X-ray flux for RRAT-bursts of <1.5e-8 ergs cm-2 s-1 (2-10 keV) or a luminosity <2.3e37 (d/3.6kpc)^2 ergs s-1. The time-average burst flux is <2e-13 ergs cm-2 s-1 (0.5-8 keV) -- a factor of 10 below that of the previously identified persistent X-ray counterpart. Thus, X-ray bursts from the RRAT are energetically unimportant compared with the persistent X-ray emission. From the previously observed burst radio flux, we derive an upper-limit F_x/F_R< 4.2e-12 erg cm-2 s-1 mJy-1 for the radio bursts from this RRAT, the most stringent to date, due to the high radio flux of bursts from this source. The F_x/F_R ratio is a factor approximately 80 larger than that of the millisecond pulsar PSR B1821-24; thus emission processes of X-ray/radio efficiency comparable to MSP pulses cannot be ruled out. However, if the RRAT burst emission mechanism is identical to the msec bursts of magnetars, then the msec bursts of magnetars should be easily detected with radio instrumentation; yet none have been reported to date.
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