Small-angle X-ray scattering (SAXS) is a powerful technique to probe nanometer-scale structures; a particularly powerful implementation of SAXS is to apply it to continuously flowing liquid samples in microfluidic devices. This approach has been employed extensively, but virtually all existing studies rely on the use of one-phase microfluidics. We overcome this limitation and present the combination of SAXS with multiphase, droplet-based microfluidics to establish a platform methodology. We focus on the use of two different classes of microfluidic devices in two different approaches. In one approach, we use silicone elastomer devices to form water-in-oil emulsion droplets that contain gold nanoparticles as a model analyte. The emulsion droplets serve as nanoliter-scale compartments that are probed by SAXS off the microfluidic chip. In another approach, we both create and probe the droplets on the same microfluidic chip. In this case, we use a glass microcapillary device that serves to form gold nanoparticles in situ by mixing two aqueous precursor fluids within the drops. Both approaches allow the gold-nanoparticle scattering to be straightforwardly isolated from the raw data; subsequent fitting yields quantitative information on the size, shape, and concentration of the nanoparticles within the compartmentalizing emulsion droplets. In addition, the microfluidic flow parameters scale with the scattering cross-sections in a quantitative fashion. These results foreshadow the utility of this technique for other, more sophisticated tasks such as single-protein analysis or automated assaying.