The surface tension of colloid-fluid spherical interfaces is calculated in the context of the Ornstein-Zernike integral equation. We study models consisting of one colloidal particle immersed in a vapor phase and in low-density fluids at supercritical conditions. This paper focuses on the calculation of the surface tension of the substrate-fluid interfaces via integral equations. We consider a methodology based on the calculation of the chemical potential of the colloid in the fluid. This idea constitutes the basis of the celebrated scaled-particle theory. Analysis of a wide range of colloidal sizes and colloid-fluid interaction strengths shows that traditional theories, such as the hypernetted chain integral equation, accurately predict the surface tension of colloid-vapor spherical interfaces of a few nanometers size. We also consider theoretical approaches which incorporate the bridge function, such as the Percus-Yevick theory. The accuracy of these theories to describe the structure of the adsorbed fluid and surface tensions of colloids immersed in fluids at different conditions is discussed.