An accurate temporal characterization of both pump and probe pulses is essential for the correct interpretation of any pump-probe experiment. This is particularly true for attosecond spectroscopy, where the pulses are too short to be directly measured with electronic devices. However, when measuring the absolute timing between a light waveform and the related photoinduced physical phenomenon, such characterization does not suffice. Here, we introduce a new method called rACE (refined Analytical Chirp Evaluation), which retrieves both pump and probe pulses while establishing a direct relation between the reconstructed time axis and the experimental delay. This feature is particularly relevant for the extraction of absolute time delays, a growing field in attosecond spectroscopy. In this work, we prove the robustness of rACE with simulated datasets involving the effect of pulse chirp, distinctive target attributes, and non-isolated attosecond pulses, which normally constitute challenging situations for standard methods. For all the cases reported here, rACE achieves a precise absolute delay calibration with an accuracy better than the atomic unit of time. Its successful application to attosecond experimental measurements makes it a fundamental tool for attaining sub-cycle absolute temporal resolution, enabling new investigations of lightwave-driven ultrafast phenomena.