Since process and environmental variations can no longer be ignored in high-performance microprocessor designs, it is necessary to develop techniques for computing the sensitivities of the timing slacks to parameter variations. This additional slack information enables designers to examine paths that have large sensitivities to various parameters: such paths are not robust, even though they may have large nominal slacks and may hence be ignored in traditional timing analysis. We present a framework for block-based timing analysis, where the parameters are specified as ranges - rather than statistical distributions which are hard to know in practice. We show that our approach - which scales well with the number of processors - is accurate at all values of the parameters within the specified bounds, and not just at the worstcase corner. This allows the designers to quantify the robustness of the design at any design point. We validate our approach on circuit blocks extracted from a commercial 45nm microprocessor.