We approach the task of detecting the illicit movement of cultural heritage from a machine learning perspective by presenting a framework for detecting a known artefact in a new and unseen image. To this end, we explore the machine learning problem of instance classification for large archaeological images datasets, i.e. where each individual object (instance) is itself a class that all of the multiple images of that object belongs. We focus on a wide variety of objects in the Durham Oriental Museum with which we build a dataset with over 24,502 images of 4332 unique object instances. We experiment with state-of-the-art convolutional neural network models, the smaller variations of which are suitable for deployment on mobile applications. We find the exact object instance of a given image can be predicted from among 4332 others with ~ 72% accuracy, showing how effectively machine learning can detect a known object from a new image. We demonstrate that accuracy significantly improves as the number of images-per-object instance increases (up to ~ 83%), with an ensemble of classifiers scoring as high as 84%. We find that the correct instance is found in the top 3, 5, or 10 predictions of our best models ~ 91%, ~ 93%, or ~ 95% of the time respectively. Our findings contribute to the emerging overlap of machine learning and cultural heritage, and highlights the potential available to future applications and research.