Simulation-based inference (SBI) provides a principled route to parameter inference when a simulator is available but pointwise likelihood evaluation is infeasible. Two technical bottlenecks nevertheless remain central in practical statistical computing: learning low-dimensional summaries that are informative for the \emph{particular} observed dataset, and delivering uncertainty regions that remain reliable after approximate inference. Existing work has substantially advanced these directions, but largely in parallel rather than jointly. This paper introduces \emph{LoCal-SBI}, a unified procedure that couples observed-data-specific summary refinement with stratified conformal calibration of posterior regions. The method first learns a pilot global map on prior-predictive simulations. For a given observation, it then localizes simulations in the pilot posterior space and refits a weighted summary map in that neighborhood. An empirical Gibbs posterior is formed over the simulated particles, and ellipsoidal credible regions are subsequently calibrated by Mondrian conformal quantiles computed within pilot-defined strata. The resulting procedure admits a transparent statistical analysis: we establish a local bias--variance bound for the learned summary map, a posterior perturbation inequality transferring summary error to posterior mean error, a finite-sample cell-conditional coverage guarantee for the calibrated regions, and a weak-misspecification bound showing that nuisance shifts enter only through the local nuisance sensitivity of the summary operator. Experiments on a curved banana benchmark, the g-and-k model, and a regime-switching nuisance-shift benchmark show that localization and calibration are complementary: localization improves posterior geometry and point accuracy, whereas conformalization restores reliability without the excessive conservatism of global baselines. Across the reported benchmarks, LoCal-SBI consistently improves posterior mean accuracy relative to globally calibrated summary baselines while producing materially smaller calibrated credible regions.