The purpose of this paper is twofold. On the methodological side, we shall attempt to show that even relatively simple and accessible experimental methods can yield significant insights into semantic issues. At the same time, we argue that experimental evidence, both the type collected in simple questionnaires and measures of on-line processing, can inform semantic theories. The specific case that we address here concerns the investigation of quantifier scope. In this area, where judgements are often subtle and controversial, the gradient data that psycholinguistic experiments provide can be a useful tool to distinguish between competing approaches, as we demonstrate with a case study. Furthermore, we describe how a modification of existing experimental methods can be used to test predictions of underspecification theories. The program of research we outline here is not intended to be a prescriptive set of instructions for researchers, telling them what they should do; rather it is intended to illustrate some problems an experimental semanticist may encounter but also the profit of this enterprise.