It has been argued in Dawid (String theory and the scientific method, Cambridge University Press, Cambridge, [4]) that physicists at times generate substantial trust in an empirically unconfirmed theory based on observations that lie beyond the theory's intended domain. A crucial role in the reconstruction of this argument of non-empirical confirmation is played by limitations to scientific underdetermination. The present paper discusses the question as to how generic the role of limitations to scientific underdetermination really is. It is argued that assessing such limitations is essential for generating trust in any theory's predictions, be it empirically confirmed or not. The emerging view suggests that empirical and non-empirical confirmation are more closely related to each other than one may expect at first glance.