We report on residual-gas damping of the motion of a macroscopic test mass enclosed in a nearby housing in the molecular flow regime. The damping coefficient, and thus the associated thermal force noise, is found to increase significantly when the distance between the test mass and surrounding walls is smaller than the test mass itself. The effect has been investigated with two torsion pendulums of different geometry and has been modeled in a numerical simulation whose predictions are in good agreement with the measurements. Relevant to a wide variety of small-force experiments, the residual-gas force noise power for the test masses in the LISA gravitational wave observatory is roughly a factor 15 larger than in an infinite gas volume, though still compatible with the target acceleration noise of 3 fm s(-2) Hz(-1/2) at the foreseen pressure below 10(-6) Pa.