[en] We derive the one-loop amplitudes for the emission of tachyons and massless bosons from closed unoriented bosonic strings. Contributions from both the torus and the Klein bottle are included, and the structure of their divergences is discussed. It is shown that in the zero-slope limit, the amplitude for emission of massless bosons agrees with results of point-field calculations for the coupling of scalar fields to gravity. Finally, the possibility of canceling the leading ultraviolet divergence for a particular gauge group is discussed and illustrated for the vacuum-energy density. (Author) 27 refs., 2 figs