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For various speech-related tasks, confidence scores from a speech recogniser are a useful measure to assess the quality of transcriptions. In traditional hidden Markov model-based automatic speech recognition (ASR) systems, confidence scores can be reliably obtained from word posteriors in decoding lattices. However, for an ASR system with an auto-regressive decoder, such as an attention-based sequence-to-sequence model, computing word posteriors is difficult. An obvious alternative is to use the decoder softmax probability as the model confidence. In this paper, we first examine how some commonly used regularisation methods influence the softmax-based confidence scores and study the overconfident behaviour of end-to-end models. Then we propose a lightweight and effective approach named confidence estimation module (CEM) on top of an existing end-to-end ASR model. Experiments on LibriSpeech show that CEM can mitigate the overconfidence problem and can produce more reliable confidence scores with and without shallow fusion of a language model. Further analysis shows that CEM generalises well to speech from a moderately mismatched domain and can potentially improve downstream tasks such as semi-supervised learning.