The most recent episode of market turmoil exposed the limitations resulting from the traditional focus on too-big-to-fail institutions within an increasingly systemic-crisis-prone financial system, and encouraged the appearance of the too-connected-to-fail (TCTF) concept. The TCTF concept conveniently broadens the base of potential destabilizing institutions beyond the traditional banking-focused approach to systemic risk, but requires methodologies capable of coping with complex, cross-dependent, context-dependent and non-linear systems. After comprehensively introducing the rise of the TCTF concept, this paper presents a robust, parsimonious and powerful approach to identifying and assessing systemic risk within payments systems, and proposes some analytical routes for assessing financial authorities´ challenges. Banco de la Republica´s approach is based on a convenient mixture of network topology basics for identifying central institutions, and payments systems simulation techniques for quantifying the potential consequences of central institutions failing within Colombian large-value payments systems. Unlike econometrics or network topology alone, results consist of a rich set of quantitative outcomes that capture the complexity, cross-dependency, context-dependency and non-linearity of payments systems, but conveniently disaggregated and dollar-denominated. These outcomes and the proposed analysis provide practical information for enhanced policy and decision-making, where the ability to measure each institution´s contribution to systemic risk may assist financial authorities in their task to achieve payments system´s stability.