The general consensus emerging from decades of empirical investigation of metaphor processing is that, when appropriately contextualised, metaphorically used language is no more demanding of processing effort than literally used language. However, there is a small number of studies which contradict this position, notably Noveck, Bianco, and Castry (2001): they maintain that relevance-based pragmatic theory predicts increased cognitive costs incurred in deriving the extra effects that metaphors typically yield, and they provide experimental results that support this prediction. In our study, we first surveyed and assessed the tasks and stimulus materials of many experiments on metaphor processing from the 1970's to the present day. The most telling result was an apparent disparity between the processing of metaphorical language used predicatively versus referentially. We then ran two self-paced reading experiments to test our hypothesis that when used as a predicate, metaphorical language is no more costly than literal language, but when used referentially, it does incur extra costs, even given a preceding biasing context. In the first experiment, all metaphorical referring expressions were in subject position so occurred early in the sentence; in the second experiment, we controlled for any effect of sentence position by placing metaphorical referring expressions in object position, thus later in the sentence, similar to the predicate metaphors. In both cases, metaphorical referring incurred significantly greater costs relative to literal equivalents than did metaphorical predication, with no effect of sentence position. We end with a brief analysis of why the referential use of metaphor is special and effort-demanding.