Testing non-inferiority in active-controlled clinical trials examines whether a new procedure is, to a pre-specified amount, no worse than an existing procedure. To assess non-inferiority between two procedures using clustered matched-pair binary data, two new statistical tests are systematically compared to existing tests. The calculation of corresponding confidence interval is also proposed. None of the tests considered requires structural within-cluster correlation or distributional assumptions. The results of an extensive Monte Carlo simulation study illustrate that the performance of the statistics depends on several factors including the number of clusters, cluster size, probability of success in the test procedure, the homogeneity of the probability of success across clusters, and the intra-cluster correlation coefficient (ICC). In evaluating non-inferiority for a clustered matched-pair study, one should consider all of these issues when choosing an appropriate test statistic. The ICC-adjusted test statistic is generally recommended to effectively control the nominal level when there is constant or small variability of cluster sizes. For a greater number of clusters, the other test statistics maintain the nominal level reasonably well and have higher power. Therefore, with the carefully designed clustered matched-pair study, a combination of the statistics investigated may serve best in data analysis. Finally, to illustrate the practical application of the recommendations, a real clustered matched-pair collection of data is used to illustrate testing non-inferiority.