In late December 1668 the Kangxi 康熙 emperor (r. 1662–1722) asked the Jesuit astronomer Ferdinand Verbiest (1623–1688) to give publicly verifiable proof that the western astronomical system introduced to China by the Jesuits was accurate. In response Verbiest proposed that he and his Chinese opponents should be set the task of predicting the length of the shadow cast by a gnomon of a given length at a given time on a given day, and his suggestion was accepted. Success in this experimental trial was vital to the future of the Jesuit mission in China. After repeating the trial at noon on three successive days, Verbiest was judged to have succeeded in showing the superiority of western methods in this respect. In this paper, we provide a detailed technical analysis of the methods used by Verbiest to make his predictions of gnomon shadows, and trace the sources of his skills back to his astronomical studies in Europe before his departure for China. In the course of this investigation, we discuss changes in European astronomical techniques up to the mid 17th century that played a decisive role in his predictive task. As a result of this analysis, we are able to explain certain previously puzzling features of Verbiest’s predictions as a rational response on his part to the contentious circumstances under which the trial was conducted.