Network meta-analysis has been an essential methodology of systematic reviews for comparative effectiveness research. The restricted maximum likelihood (REML) method is one of the current standard inference methods for multivariate, contrast-based meta-analysis models, but recent studies have revealed the resultant confidence intervals of average treatment effect parameters in random-effects models can seriously underestimate statistical errors; that is, the actual coverage probability of a true parameter cannot retain the nominal level (e.g., 95%). In this article, we provided improved inference methods for the network meta-analysis and meta-regression models using higher-order asymptotic approximations based on the approach of Kenward and Roger ("Biometrics" 1997;53:983-997). We provided two corrected covariance matrix estimators for the REML estimator and improved approximations for its sample distribution using a t-distribution with adequate degrees of freedom. All of the proposed procedures can be implemented using only simple matrix calculations. In simulation studies under various settings, the REML-based Wald-type confidence intervals seriously underestimated the statistical errors, especially in cases of small numbers of trials meta-analyzed. By contrast, the proposed Kenward-Roger--type inference methods consistently showed accurate coverage properties under all the settings considered in our experiments. We also illustrated the effectiveness of the proposed methods through applications to two real network meta-analysis datasets.