Legitimacy screening, the process of verifying the identity and purpose of customers ordering synthetic nucleic acids, is a primary safeguard against the misuse of synthetic biology. However, the associated costs discourage the adoption of screening practices. To evaluate whether AI tools can facilitate this process, we tested five large language models on five verification tasks using customer profiles of life sciences researchers from around the world. We compared AI performance against an expert human baseline on flag accuracy, source quality, source fidelity, and cost. The best-performing model, Gemini 2.5 Pro aided by four bibliographic and sanctions APIs, achieved comparable flag accuracy to the human baseline (90% and 89%, respectively). Gemini 2.5 Pro outperformed the human baseline on source quality and fidelity, at roughly one-tenth of the cost ($1.18 vs. $14.04 per customer). For information-gathering tasks, which excluded the human review step, costs averaged $0.23 per customer, around 50 times cheaper than human screening. These results support piloting AI-assisted legitimacy screening at providers of synthetic nucleic acids and other dual-use biotechnology products, with AI systems handling information gathering and human reviewers retaining authority over order fulfillment decisions.