I describe the computation of energy widths of nuclear states using an integral over the interaction region of ab initio variational Monte Carlo wave functions, and I present calculated widths for many states. I begin by presenting relations that connect certain short-range integrals to widths. I then present predicted widths for 5 <= A <= 9 nuclei, and I compare them against measured widths. They match the data more closely and with less ambiguity than estimates based on spectroscopic factors. I consider the consequences of my results for identification of observed states in ^8B, ^9He, and ^9Li. I also examine failures of the method and conclude that they generally involve broad states and variational wave functions that are not strongly peaked in the interaction region. After examining bound-state overlap functions computed from a similar integral relation, I conclude that overlap calculations can diagnose cases in which computed widths should not be trusted.Comment: 26 pages, 9 figures, submitted to Phys. Rev.