Porous metal-organic frameworks have emerged as promising materials for the capture of carbon dioxide (CO2) and its separation from methane (CH4) during the industrially-important “sweetening” of sour natural-gas. The excellent thermal and chemical stability of the highly-porous UiO-66(Zr) material, combined with good selectivity for CO2 over CH4, makes this material a prime candidate for such applications. Using a combination of neutron powder-diffraction and density-functional theory, we examine the details of the binding of CO2 and CH4 in UiO-66(Zr) over the industrially-relevant 3.6 to 9.0 mmol/g concentration range, corresponding to the material that is half to fully saturated with CO2. This work builds on the previously-reported preferred site for CO2 and CH4 in UiO-66(Zr), establishing further sites and determining the strength and nature of the guest-host interaction at these. We find the UiO-66(Zr)···CO2 interactions are significantly affected by the concentration of CO2 as the binding of CO2 is enhanced by interguest interactions.