We report the results of a pilot study investigating whether the technique of Magnitude Estimation, widely used in psychophysics but also in syntax and phonology, can be exploited in discourse pragmatics. In this domain, unacceptable data (i.e. data labeled ‘#’) play an important role but acceptability judgments can be subtle, context-dependent, and thus a topic of debate, as shown by endless disputes in the literature. Using two sets of data, (in)felicitous topicalizations from Birner and Ward (1998) and the (in)felicitous use of appositive relative clauses as discussed in Loock (2010a, 2010b) on the fame effect, we aim to determine whether the Magnitude Estimation technique can provide reliable results that would overcome the difficulties with intuitive acceptability judgments. We discuss whether this technique provides acceptability judgments that are less problematic than those obtained introspectively or via regular questionnaires.