Process-induced variability is a growing concern in the design of analog circuits, and in particular for monolithic microwave integrated circuits (MMICs) targeting the 5G and 6G communication systems. The RF and microwave (MW) technologies developed for the deployment of these communication systems exploit devices whose dimension is now well below 100 nm, featuring an increasing variability due to the fabrication process tolerances and the inherent statistical behavior of matter at the nanoscale. In this scenario, variability analysis must be incorporated into circuit design and optimization, with ad hoc models retaining a direct link to the fabrication process and addressing typical MMIC nonlinear applications like power amplification and frequency mixing. This paper presents a flexible procedure to extract black-box models from accurate physics-based simulations, namely TCAD analysis of the active devices and EM simulations for the passive structures, incorporating the dependence on the most relevant fabrication process parameters. We discuss several approaches to extract these models and compare them to highlight their features, both in terms of accuracy and of ease of extraction. We detail how these models can be implemented into EDA tools typically used for RF and MMIC design, allowing for fast and accurate statistical and yield analysis. We demonstrate the proposed approaches extracting the black-box models for the building blocks of a power amplifier in a GaAs technology for X-band applications.