In real-world applications across specialized domains, addressing complex out-of-distribution (OOD) challenges is a common and significant concern. In this study, we concentrate on the task of fine-grained bronze ware dating, a critical aspect in the study of ancient Chinese history, and developed a benchmark dataset named ShiftedBronzes. By extensively expanding the bronze Ding dataset, ShiftedBronzes incorporates two types of bronze ware data and seven types of OOD data, which exhibit distribution shifts commonly encountered in bronze ware dating scenarios. We conduct benchmarking experiments on ShiftedBronzes and five commonly used general OOD datasets, employing a variety of widely adopted post-hoc, pre-trained Vision Large Model (VLM)-based and generation-based OOD detection methods. Through analysis of the experimental results, we validate previous conclusions regarding post-hoc, VLM-based, and generation-based methods, while also highlighting their distinct behaviors on specialized datasets. These findings underscore the unique challenges of applying general OOD detection methods to domain-specific tasks such as bronze ware dating. We hope that the ShiftedBronzes benchmark provides valuable insights into both the field of bronze ware dating and the and the development of OOD detection methods. The dataset and associated code will be available later.