Large language models (LLMs) are prone to hallucinations and sensitive to prompt perturbations, often resulting in inconsistent or unreliable generated text. Different methods have been proposed to mitigate such hallucinations and fragility, one of which is to measure the consistency of LLM responses–the model’s confidence in the response or likelihood of generating a similar response when resampled. In previous work, measuring LLM response consistency often relied on calculating the probability of a response appearing within a pool of resampled responses, analyzing internal states, or evaluating logits of resopnses. However, it was not clear how well these approaches approximated users’ perceptions of consistency of LLM responses. To find out, we performed a user study (n=2,976) demonstrating that current methods for measuring LLM response consistency typically do not align well with humans’ perceptions of LLM consistency. We propose a logit-based ensemble method for estimating LLM consistency and show that our method matches the performance of the best-performing existing metric in estimating human ratings of LLM consistency. Our results suggest that methods for estimating LLM consistency without human evaluation are sufficiently imperfect to warrant broader use of evaluation with human input; this would avoid misjudging the adequacy of models because of the imperfections of automated consistency metrics.