Conformance proportions, which are often employed in quality control, environmental monitoring, and many other areas, are important indices for evaluating product quality and process capability. When the population of interest is assumed to have a normal mixture distribution and specification limits are set by a quality engineer, estimating conformance proportions can be a practical issue. Under the framework of normal mixture distributions, a new method is proposed in this study to obtain confidence intervals for conformance proportions. More specifically, a Markov chain Monte Carlo sampler is developed to generate realizations from the generalized fiducial distributions. The required interval estimates can then be calculated by using the obtained realizations. A real-world environmental monitoring example is used to demonstrate that the proposed method is feasible in practice. Based on simulation results, it is shown that the proposed method can maintain the empirical coverage rate sufficiently close to the nominal level.