Non-inferiority tests for matched-pair data where pairs are mutually independent may not be appropriate when pairs are clustered. The tests may require an adjustment to account for the correlation within a cluster. We consider the adjusted score and Wald-type tests, and a modification of Obuchowski's method for non-inferiority and compare them with the non-inferiority test based on a method of moments estimate in terms of Type 1 error rate and power by simulations for a small cluster size under various correlation structures. In general, the score test adjusted by an inflation factor and the modified Obuchowski's method perform as good as the test based on moments estimate in the accuracy of Type 1 error rates. The latter does not provide reasonably close Type 1 error rates to the nominal level when the number of clusters is 25 or smaller and a positive response rate for the standard procedure is 20 per cent or lower. The adjusted score test, the method based on moments estimate and the modified test are comparable in power. The adjusted Wald-type test is too anti-conservative and we should caution use of the test. Since number of clusters is strongly related to the accuracy of empirical Type 1 error rate and power, it is very important to have a sufficiently large number of clusters in designing a clustered matched-pair study for non-inferiority.