Herringbone grooved journal bearings (HGJBs) are widely used in micro-turbocompressor applications due to their high load-carrying capacity, low friction, and oil-free solution. However, the performance of these bearings is sensitive to manufacturing deviations, which can lead to significant variations in their performance and stability. In this study, design guidelines for robust design against manufacturing deviations of HGJB supported micro-turbocompressors are proposed. These guidelines are based on surrogate model assisted multi-objective optimization using ensembles of artificial neural networks trained on a large dataset of rotor and bearing designs as well as operating conditions. The developed framework is then applied to a series of case studies representative of heat-pump and fuel cell micro-turbomachines. To highlight the importance of rotor geometry and bearing aspect ratio in the robustness of HGJBs, two types of optimizations are performed: one focusing on optimizing the bearing geometry, and the other focusing on both the bearing and rotor geometries. The analysis of the Pareto fronts and Pareto optima of each type of optimization and case study allows for the derivation of design guidelines for the robust design of HGJB supported rotors. Results suggest that by following these guidelines, it is possible to significantly improve the robustness of herringbone grooved journal bearings against manufacturing deviations, resulting in stable operation. The best design achieved $\pm\SI{8}{\micro\meter}$ tolerance on the bearing clearance, and designs optimized for both rotor and bearing geometry outperformed those optimized for bearing geometry alone. This work successfully identifies guidelines for the robust design of herringbone grooved journal bearings in micro-turbocompressor applications, demonstrating the strength of surrogate model assisted multi-objective optimization. It provides a valuable tool for engineers seeking to optimize the performance and reliability of these bearings.