Counterspeech has emerged as a popular and effective strategy for combating online hate speech, sparking growing research interest in automating its generation using language models. However, the field still lacks standardised evaluation protocols and reliable automated evaluation metrics that align with human judgement. Current automatic evaluation methods, primarily based on similarity metrics, do not effectively capture the complex and independent attributes of counterspeech quality, such as contextual relevance, aggressiveness, or argumentative coherence. This has led to an increased dependency on labor-intensive human evaluations to assess automated counter-speech generation methods. To address these challenges, we introduce CSEval, a novel dataset and framework for evaluating counterspeech quality across four dimensions: contextual-relevance, aggressiveness, argument-coherence, and suitableness. Furthermore, we propose Auto-Calibrated COT for Counterspeech Evaluation (Auto-CSEval), a prompt-based method with auto-calibrated chain-of-thoughts (CoT) for scoring counterspeech using large language models. Our experiments show that Auto-CSEval outperforms traditional metrics like ROUGE, METEOR, and BertScore in correlating with human judgement, indicating a significant improvement in automated counterspeech evaluation.