Cancers arise as the result of somatically acquired changes in the DNA of cancer cells. However, in addition to the mutations that confer a growth advantage, cancer genomes accumulate a large number of somatic mutations resulting from normal DNA damage and repair processes as well as carcinogenic exposures or cancer related aberrations of DNA maintenance machinery. These mutagenic processes often produce characteristic mutational patterns called mutational signatures. The decomposition of a cancer genome's mutation catalog into mutations consistent with such signatures can provide valuable information about cancer etiology. However, the results from different decomposition methods are not always consistent. Hence, one needs to be able to not only decompose a patient's mutational profile into signatures but also establish the accuracy of such decomposition.Results: We proposed two complementary ways of measuring confidence and stability of decomposition results and applied them to analyze mutational signatures in breast cancer genomes. We identified both very stable and highly unstable signatures, as well as signatures that previously have not been associated with breast cancer. We also provided additional support for the novel signatures. Our results emphasize the importance of assessing the confidence and stability of inferred signature contributions.Availability: All tools developed in this paper have been implemented in an R package, called SignatureEstimation, which is available from https://www.ncbi.nlm.nih.gov/CBBresearch/Przytycka/index.cgi#signatureestimation.