Scientific expert testimony is crucial to public deliberation, but it is associated with many pitfalls. This article identifies one—namely, expert trespassing testimony—which may be characterized, crudely, as the phenomenon of experts testifying outside their domain of expertise. My agenda is to provide a more precise characterization of this phenomenon and consider its ramifications for the role of science in society. I argue that expert trespassing testimony is both epistemically problematic and morally problematic. Specifically, I will argue that scientific experts are (...) subject to a particular obligation. Roughly, this is the obligation to qualify their assertions when speaking outside their domain of scientific expertise in certain contexts. Thus, I argue that scientists who possess expert knowledge are confronted with hard questions about when and how to testify and, therefore, that being a scientific expert comes with great responsibility. Consequently, I provide a concrete “expert guideline” according to which scientific experts, in certain contexts, face an obligation to qualify their assertions when speaking outside their domain of expertise. Furthermore, I consider a number of the conditions in which the guideline is waived or overridden. On this basis, I consider the broader aspects of the roles of scientific experts in a society with a high division of cognitive labor that calls for trust in scientific expert testimony. (shrink)