Despite the large number of metal-organic frameworks that have been studied in the context of post-combustion carbon capture, adsorption equilibria of gas mixtures including CO2, N-2, and H2O, which are the three biggest components of the flue gas emanating from a coal- or natural gas-fired power plant, have never been reported. Here, we disclose the design and validation of a high-throughput multicomponent adsorption instrument that can measure equilibrium adsorption isotherms for mixtures of gases at conditions that are representative of an actual flue gas from a power plant. This instrument is used to study 15 different metal-organic frameworks, zeolites, mesoporous silicas, and activated carbons representative of the broad range of solid adsorbents that have received attention for CO2 capture. While the multicomponent results presented in this work provide many interesting fundamental insights, only adsorbents functionalized with alkylamines are shown to have any significant CO2 capacity in the presence of N-2 and H2O at equilibrium partial pressures similar to those expected in a carbon capture process. Most significantly, the amine-appended metal organic framework mmen-Mg-2(dobpdc) (mmen = N,N'-dimethylethylenediamine, dobpdc (4-) = 4,4'-dioxido-3,3'-biphenyldicarboxylate) exhibits a record CO2 capacity of 4.2 +/- 0.2 mmol/g (16 wt %) at 0.1 bar and 40 degrees C in the presence of a high partial pressure of H2O.