Liquid cells are an increasingly common sample environment for neutron reflectometry experiments and are critical for measuring the properties of materials at solid/liquid interfaces. Background scattering determines the maximum useful scattering vector, and hence the spatial resolution, of the neutron reflectometry measurement. The primary sources of background are the liquid in the cell reservoir and the materials forming the liquid cell itself. Thus, characterization and mitigation of these background sources are necessary for improvements in the signal-to-background ratio and resolution of neutron reflectometry measurements employing liquid cells. Single-crystal silicon is a common material used for liquid cells due to its low incoherent scattering cross section for neutrons, and the path lengths of the neutron beam through silicon can be several centimetres in modern cell designs. Here, a liquid cell is constructed with a sub-50 µm thick liquid reservoir encased in single-crystal silicon. It is shown that, at high scattering vectors, inelastic scattering from silicon represents a significant portion of the scattering background and is, moreover, structured, confounding efforts to correct for it by established background subtraction techniques. A significant improvement in the measurement quality is achieved using energy-analyzed detection. Energy-analyzed detection reduces the scattering background from silicon by nearly an order of magnitude, and from fluids such as air and liquids by smaller but significant factors. Combining thin liquid reservoirs with energy-analyzed detection and the high flux of the CANDOR polychromatic reflectometer at the NIST Center for Neutron Research, a background-subtracted neutron reflectivity smaller than 10−8 from a liquid cell sample is reported.