Many constructs that characterize language, like its complexity or emotionality, have a naturally continuous semantic structure; a public speech is not just “simple” or “complex”, but exists on a continuum between extremes. Although large language models (LLMs) are an attractive tool for measuring scalar constructs, their idiosyncratic treatment of numerical outputs raises questions of how to best apply them. We address these questions with a comprehensive evaluation of LLM-based approaches to scalar construct measurement in social science. Using multiple datasets sourced from the political science literature, we evaluate four approaches: unweighted direct pointwise scoring, aggregation of pairwise comparisons, token-probability-weighted pointwise scoring, and finetuning. Our study finds that pairwise comparisons made by LLMs produce better measurements than simply prompting the LLM to directly output the scores, which suffers from bunching around arbitrary numbers. However, taking the weighted mean over the token probability of scores further improves the measurements over the two previous approaches. Finally, finetuning smaller models with as few as 1,000 training pairs can match or exceed the performance of prompted LLMs.