Computer simulations have long posed the exciting possibility for scientific insight into complex real-world processes. However, despite the power of modern computing, it remains challenging to systematically perform inference under simulation models. This has led to the rise of simulation-based inference (SBI), a class of machine learning-enabled techniques for approaching inverse problems under stochastic simulation-based models. Many such methods, however, require large numbers of simulation samples and face difficulty scaling to high-dimensional settings, often making inference prohibitive under resource-intensive simulators. To mitigate these drawbacks, we introduce active sequential neural posterior estimation (ASNPE). ASNPE integrates an active learning scheme to estimate the utility of simulation parameter candidates to the underlying probabilistic model. The proposed acquisition is easily integrated into existing posterior estimation pipelines, allowing for improved sample efficiency with low computational overhead. We further demonstrate the effectiveness of the proposed method in the urban demand calibration setting, a high-dimensional inverse problem commonly requiring computationally expensive traffic simulators. Our method is demonstrated to outperform well-tuned benchmarks and other posterior estimation methods on a large-scale real-world traffic network.