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As a class of approximate measurement approaches, sketching algorithms have significantly improved the estimation of network flow information using limited resources. While these algorithms enjoy sound error-bound analysis under worst-case scenarios, their actual errors can vary significantly with the incoming flow distribution, making their traditional error bounds too "loose" to be useful in practice. In this paper, we propose a simple yet rigorous error estimation method to more precisely analyze the errors for posterior sketch queries by leveraging the knowledge from the sketch counters. This approach will enable network operators to understand how accurate the current measurements are and make appropriate decisions accordingly (e.g., identify potential heavy users or answer "what-if" questions to better provision resources). Theoretical analysis and trace-driven experiments show that our estimated bounds on sketch errors are much tighter than previous ones and match the actual error bounds in most cases.