Meta-analyses, like primary studies, are affected by researcher degrees of freedom: researchers must decide which studies to include, how to compute effect sizes, and which statistical models to use. Different reasonable choices can lead to different results, making multiverse meta-analysis a useful tool for assessing robustness across alternative specifications. However, multiverse meta-analysis also introduces a multiple-testing problem. Current inferential approaches mainly provide a global test, which can establish that at least one specification differs from the null but cannot identify which individual specifications do so while accounting for multiplicity across the full multiverse. We introduce Post-selection Inference in Multiverse Meta-Analysis (PIMMA), which allows inference on individual specifications while controlling the Family-Wise Error Rate (FWER) and accounting for their dependence. In practical terms, PIMMA shows which results remain statistically significant after accounting for multiplicity across all reasonable analytical choices. In simulations, the specification-level test adequately controlled Type I error, with power comparable to robust variance estimation in scenarios where both methods maintained appropriate Type I error control. In an application to meta-analyses of Cognitive Behavioral Therapy efficacy for adult depression, 297 of 336 unique meta-analytic analyses remained significant after step-down max-T adjustment for multiple testing, accounting for dependence among analyses. PIMMA therefore extends multiverse meta-analysis from a global assessment of whether any effect is present to specification-level inference, allowing researchers to evaluate robustness across specifications and identify which individual results remain significant under appropriate error control.