Sulfur, omnipresent in fossil fuels and biomass, causes substantial industrial challenges and significant environmental harm when released to the atmosphere. Efficient and cost-effective integration of sulfur removal into high-temperature industrial processes calls for temperature compatible strategies, and solid sorbents offer the most promising solution. This article presents C-H-O ternary diagrams as visual tools for fundamental evaluation of potential sulfur uptake capacity of solid sorbents. The findings of this study are based on thermodynamic analyses and highlight how the C/H/O ratio of the fuel feedstock as well as the gasification or oxidation agent affect sulfur uptake capacity of the sorbents. The thermodynamic effect of changing temperature (T = 1000-1400 K) and pressure (P = 1-10 atm) on sorbent sulfur uptake is also explored. In this study, Ca- and Sr-based sorbents are investigated, but C-H-O ternary diagrams could be calculated for any other potential solid sorbent. Important thermodynamic insights are drawn from the C-H-O ternary equilibria. Importantly, the initial sulfur content of the fuel does not affect the thermodynamic limit of the sorbent, which is primarily a function of the overall C/H/O ratio of the fuel + gasification or oxidation agent. Under reducing conditions, the total gas-phase sulfur concentration depends strongly on the water vapor partial pressure. Moreover, operating at stoichiometric oxygen conditions results in poor sorbent sulfur uptake with a rapid rise in SO2 mole fraction. The article also offers important insights to predict the most favorable conditions for the use of solid sorbents that can mitigate anode deactivation in solid oxide-based carbon fuel cells.