Fuel cells are considered one of the most efficient and environmental-friendly technologies available for converting chemical energy into electricity and heat, and considered a key technology to close the hydrogen cycle. In particular, combined heat and power (CHP) plants based on intermediate solid oxide fuel cells (SOFC) are of interest for their fuel flexibility (e.g. biogenic fuels), near market readiness, and high potential for coupling to existing systems due to the high-energy off-gases (high temperatures, highly reactive gases). Under SOFC operating conditions, small-scale gas bearing supported turbomachinery are of interest as Balance of Plant (e.g. as coupling device with up- or downstream systems) and for system performance enhancement (e.g. for off-gas recirculation), as they are oil-free (no risk of catalyst contamination), offer a high lifetime (no mechanical wear), are able to cope with high temperatures, are flexible and allow for continuous operation. However, despite many theoretical advances in the SOFC and turbomachinery domains, the design, realization and operation of SOFC-turbomachinery systems for green CHP generation is still an experimentally and economically challenging task. This is due to the high system complexity, challenging control, and in particular, the currently not well-understood interdependencies between the system components, such as between the SOFC and turbomachinery, especially regarding their individual safe operating windows. This thesis addresses these issues with a holistic and interdisciplinary approach, by discussing different SOFC-turbomachinery system concepts and layouts, as well as by applying and advancing field-specific tools and methodologies for system- and component-level analyses from multiple domains, spanning from electrochemistry and computational thermodynamics to aerodynamics and artificial neural networks. The key scientific contributions of this work are: (i) novel SOFC plant layouts with optimal off-gas integration and treatment via high-temperature turbomachinery and compatible carbon capture and storage technologies; (ii) novel carbon formation risk maps based on the normalized chemical activity that facilitate the exploration and comparison of innovative SOFC stack and system design solutions while ensuring safe operation; (iii) a novel experimentally validated holistic design methodology and improved 1D meanline models for gas bearing supported turbomachinery in SOFC applications; and (iv) a novel working prototype of a high-temperature, steam-driven, gas bearing supported compressor-turbine-unit for SOFC-CHP systems featuring a high robustness towards off-design conditions and manufacturing deviations. The contributions of this work support the implementation and fast prototyping of future small-scale SOFC-CHP plants with high-temperature turbomachinery for enhanced stack and system performances, extended safe operating windows, and carbon-neutral or -negative emission power and heat. The developed tools and methodologies go beyond navigating the complex landscape of proposing a viable turbomachinary design for SOFC applications, and improve the toolkit for engineers tackling similar tasks of such interdisciplinary nature.