Calibrating Agent-Based Models (ABMs) is an important optimization problem for simulating the complex social systems, where the goal is to identify the optimal parameter of a given ABM by minimizing the discrepancy between the simulated data and the real-world observations. Unfortunately, it suffers from the extensive computational costs of iterative evaluations, which involves the expensive simulation with the candidate parameter. While Surrogate-Assisted Evolutionary Algorithms (SAEAs) have been widely adopted to alleviate the computational burden, existing methods face two key limitations: 1) surrogating the original evaluation function is hard due the nonlinear yet multi-modal nature of the ABMs, and 2) the commonly used surrogates cannot share the optimization experience among multiple calibration tasks, making the batched calibration less effective. To address these issues, this work proposes Automatic posterior transformation with Negatively Correlated Search and Adaptive Trust-Region (ANTR). ANTR first replaces the traditional surrogates with a pretrainable neural density estimator that directly models the posterior distribution of the parameters given observed data, thereby aligning the optimization objective with parameter-space accuracy. Furthermore, we incorporate a diversity-preserving search strategy to prevent premature convergence and an adaptive trust-region method to efficiently allocate computational resources. We take two representative ABM-based financial market simulators as the test bench as due to the high non-linearity. Experiments demonstrate that the proposed ANTR significantly outperforms conventional metaheuristics and state-of-the-art SAEAs in both calibration accuracy and computational efficiency, particularly in batch calibration scenarios across multiple market conditions.