This paper introduces NoRefER, a novel referenceless quality metric for automatic speech recognition (ASR) systems. Traditional reference-based metrics for evaluating ASR systems require costly ground-truth transcripts. NoRefER overcomes this limitation by fine-tuning a multilingual language model for pair-wise ranking ASR hypotheses using contrastive learning with Siamese network architecture. The self-supervised NoRefER exploits the known quality relationships between hypotheses from multiple compression levels of an ASR for learning to rank intra-sample hypotheses by quality, which is essential for model comparisons. The semi-supervised version also uses a referenced dataset to improve its inter-sample quality ranking, which is crucial for selecting potentially erroneous samples. The results indicate that NoRefER correlates highly with reference-based metrics and their intra-sample ranks, indicating a high potential for referenceless ASR evaluation or a/b testing.