Abstention Ability (AA) is a critical aspect of Large Language Model (LLM) reliability, referring to an LLM’s capability to withhold responses when uncertain or lacking a definitive answer, without compromising performance. Although previous studies have attempted to improve AA, they lack a standardized evaluation method and remain unsuitable for black-box models where token prediction probabilities are inaccessible. This makes comparative analysis challenging, especially for state-of-the-art closed-source commercial LLMs. This paper bridges this gap by introducing a black-box evaluation approach and a new dataset, Abstain-QA, crafted to rigorously assess AA across varied question types (answerable and unanswerable), domains (well-represented and under-represented), and task types (fact-centric and reasoning). We also propose a new confusion matrix, the ”Answerable-Unanswerable Confusion Matrix” (AUCM) which serves as the basis for evaluating AA, by offering a structured and precise approach for assessment. Finally, we explore the impact of three prompting strategies — Strict Prompting, Verbal Confidence Thresholding, and Chain-of-Thought (CoT) — on improving AA. Our results indicate that even powerful models like GPT-4, Mixtral 8x22b encounter difficulties with abstention; however, strategic approaches such as Strict prompting and CoT can enhance this capability.