Analysing and predicting the advance rate of a tunnel boring machine (TBM) in hard rock is integral to tunnelling project planning and execution. It has been applied in the industry for several decades with varying success. Most prediction models are based on or designed for large-diameter TBMs, and much research has been conducted on related tunnelling projects. However, only a few models incorporate information from projects with an outer diameter smaller than 5 m and no penetration prediction model for pipe jacking machines exists to date. In contrast to large TBMs, small-diameter TBMs and their projects have been considered little in research. In general, they are characterised by distinctive features, including insufficient geotechnical information, sometimes rather short drive lengths, special machine designs and partially concurring lining methods like pipe jacking and segment lining. A database which covers most of the parameters mentioned above has been compiled to investigate the performance of small-diameter TBMs in hard rock. In order to provide sufficient geological and technical variance, this database contains 37 projects with 70 geotechnically homogeneous areas. Besides the technical parameters, important geotechnical data like lithological information, unconfined compressive strength, tensile strength and point load index is included and evaluated. The analysis shows that segment lining TBMs have considerably higher penetration rates in similar geological and technical settings mostly due to their design parameters. Different methodologies for predicting TBM penetration, including state-of-the-art models from the literature as well as newly derived regression and machine learning models, are discussed and deployed for backward modelling of the projects contained in the database. New ranges of application for small-diameter tunnelling in several industry-standard penetration models are presented, and new approaches for the penetration prediction of pipe jacking machines in hard rock are proposed.