Substrate noise (SN) is an important problem in mixed-signal designs. With increasing design complexity, it is not possible to simulate for SN with a detailed SPICE model that uses an accurate model for each transistor. In this paper, we propose a sensitivity analysis- and static timing analysis-based methodology to derive a reduced model that computes the worst case substrate noise in the design. The reduced model contains only passive components, which are very few, and is very quick to simulate. The main feature of our methodology is that, unlike previous approaches, it is independent of input patterns and does not need to simulate for millions of clock cycles. This lets us apply it to a full-chip design in reasonable CPU time. We validate our reduced model on several benchmark circuits against a detailed and highly accurate reference model. On average, the reduced model is within 16.4% of the reference model and is up to 38 times faster. Finally, we apply our methodology to a mixed-signal switch chip design consisting of 8 million gates and show that it finishes in 17 minutes.