Statistical methods for testing and interval estimation of the ratio of marginal probabilities in the matched-pair setting are considered in this paper. We are especially interested in the situation where the null value is not one, as in one-sided equivalence trials. We propose a Fieller-type statistic based on constrained maximum likelihood (CML) estimation of nuisance parameters. For a series of examples, the significance level of the CML test is satisfactorily close to the nominal level, while a Wald-type test is anticonservative for reasonable sample sizes. We present formulae for approximate power and sample size for the CML and Wald tests. The matched design is seen to have a clear advantage over the unmatched design in terms of asymptotic efficiency when the two responses of the pair are highly positively correlated. We recommend the CML method over the Wald method, especially for small or moderate sample sizes.