The surface tension of interacting polymers in a good solvent is calculated theoretically and by computer simulations for a planar wall geometry and for the insertion of a single colloidal hard sphere. This is achieved for the planar wall and for the larger spheres by an adsorption method, and for smaller spheres by a direct insertion technique. Results for the dilute and semidilute regimes are compared to results for ideal polymers, the Asakura-Oosawa penetrable-sphere model, and to integral equations, scaling and renormalization group theories. The largest relative changes with density are found in the dilute regime, so that theories based on noninteracting polymers rapidly break down. A recently developed "soft colloid" approach to polymer-colloid mixtures is shown to correctly describe the one-body insertion free-energy and the related surface tension.