Systematic reviews are crucial for evidence-based medicine as they comprehensively analyse published research findings on specific questions. Conducting such reviews is often resource- and time-intensive, especially in the screening phase, where abstracts of publications are assessed for inclusion in a review. This study investigates the effectiveness of using zero-shot large language models (LLMs) for automatic screening. We evaluate the effectiveness of eight different LLMs and investigate a calibration technique that uses a predefined recall threshold to determine whether a publication should be included in a systematic review. Our comprehensive evaluation using five standard test collections shows that instruction fine-tuning plays an important role in screening, that calibration renders LLMs practical for achieving a targeted recall, and that combining both with an ensemble of zero-shot models saves significant screening time compared to state-of-the-art approaches.