In this paper, we describe SemEval-2013 Task 4: the definition, the data, the evaluation and the results. The task is to capture some of the meaning of English noun compounds via paraphrasing. Given a two-word noun compound, the participating system is asked to produce an explicitly ranked list of its free-form paraphrases. The list is automatically compared and evaluated against a similarly ranked list of paraphrases proposed by human annotators, recruited and managed through Amazon's Mechanical Turk. The comparison of raw paraphrases is sensitive to syntactic and morphological variation. The "gold" ranking is based on the relative popularity of paraphrases among annotators. To make the ranking more reliable, highly similar paraphrases are grouped, so as to downplay superficial differences in syntax and morphology. Three systems participated in the task. They all beat a simple baseline on one of the two evaluation measures, but not on both measures. This shows that the task is difficult.