Large Language Models (LLMs) offer natural language explanations as an alternative to feature attribution methods for model interpretability. However, despite their plausibility, they may not reflect the model's internal reasoning faithfully, which is crucial for understanding the model's true decision-making processes. Although several faithfulness metrics have been proposed, a unified evaluation framework remains absent. Here, we present Causal Diagnosticity, a framework to evaluate faithfulness metrics for natural language explanations. Our framework employs the concept of diagnosticity, and uses model-editing methods to generate faithful-unfaithful explanation pairs. Our benchmark includes four tasks: fact-checking, analogy, object counting, and multi-hop reasoning. We evaluate a prominent faithfulness metrics, including post-hoc explanation and chain-of-thought-based methods. We find that diagnostic performance varies across tasks and models, with Filler Tokens performing best overall. Additionally, continuous metrics are generally more diagnostic than binary ones but can be sensitive to noise and model choice. Our results highlight the need for more robust faithfulness metrics.