Neural Information Retrieval (NIR) has significantly improved upon heuristic-based Information Retrieval (IR) systems. Yet, failures remain frequent, the models used often being unable to retrieve documents relevant to the user's query. We address this challenge by proposing a lightweight abstention mechanism tailored for real-world constraints, with particular emphasis placed on the reranking phase. We introduce a protocol for evaluating abstention strategies in black-box scenarios (typically encountered when relying on API services), demonstrating their efficacy, and propose a simple yet effective data-driven mechanism. We provide open-source code for experiment replication and abstention implementation, fostering wider adoption and application in diverse contexts.