This paper analyses X-ray observations by the Chandra X-ray Observatory of CXOGBS J174614.3-321949 (CXB3) and CXOGBS J173620.2-293338 (CX332), two symbiotic binary star candidates identified by the Galactic Bulge Survey. Using new Chandra observations, we improved their X-ray positional uncertainties to 0.24 and 0.92 arcsec, respectively, confidently associating them with single optical counterparts. In particular, new observations of symbiotic X-ray candidate CX332 further solidify confidence in its coincidence with a carbon star. We demonstrate X-ray variability in both targets with a more recent observation of CX332 showing a decrease in brightness by a factor of 30, while CXB3 observations show it usually in a quiescent state with a factor-of-6 flare-like event in the final observations. In a combined spectral fit for CXB3, we find an NH value of $\sim (2\!-\! 3) \times 10^{22}\, \rm {cm}^{-2}$ with a Γ value of $1.5^{+0.2}_{-0.2}$ for a power-law fit and kT$10.6_{-2.9}^{+5.7}$ keV for an APEC fit and an estimated luminosity of ~8.4 × 1032 erg s-1. Spectra of CXB3 would be consistent with thermal emission as seen in white dwarf symbiotic systems, but the high X-ray luminosity in the light curve is more typically seen in symbiotic X-ray binary systems. Optical spectra of both objects taken with Gemini GMOS indicate CXB3 as containing an M-type star and CX332 having a carbon star counterpart. Both targets show at most marginal evidence of H α emission favouring a symbiotic X-ray binary interpretation for both sources, though we cannot rule out a white dwarf for either case.