The fitting of high-resolution structures into low-resolution densities obtained from techniques such as electron microscopy or small-angle X-ray scattering can yield powerful new insights. While several algorithms for achieving optimal fits have recently been developed, relatively little effort has been devoted to developing objective measures for judging the quality of the resulting fits, in particular with regard to the danger of overfitting. Here, a general method is presented for obtaining confidence intervals for atomic coordinates resulting from fitting of atomic resolution domain structures into low-resolution densities using well established statistical tools. It is demonstrated that the resulting confidence intervals are sufficiently accurate to allow meaningful statistical tests and to provide tools for detecting potential overfitting.