In this paper, we propose constructing confidence sets for a break date in cointegrating regressions by inverting a test for the break location, which is obtained by maximizing the weighted average of power. It is found that the limiting distribution of the test depends on the number of I(1) regressors whose coefficients sustain structural change and the number of I(1) regressors whose coefficients are fixed throughout the sample. By Monte Carlo simulations, we then show that compared with a confidence interval developed by using the existing method based on the limiting distribution of the break point estimator under the assumption of the shrinking shift, the confidence set proposed in the present paper has a more accurate coverage rate, while the length of the confidence set is comparable. By using the method developed in this paper, we then investigate the cointegrating regressions of Russian macroeconomic variables with oil prices with a break.