Recent work has shown that Large Language Models (LLMs) are not only a suitable tool for code generation but also capable of generating annotation-based code specifications. Scaling these methodologies may allow us to deduce provable correctness guarantees for large-scale software systems. In comparison to other LLM tasks, the application field of deductive verification has the notable advantage of providing a rigorous toolset to check LLM-generated solutions. This short paper provides early results on how this rigorous toolset is best used to reliably elicit correct specification annotations from an unreliable LLM oracle.