Abstract: This study describes an algorithm for determining the fine phase response of equivalent sampling oscilloscopes of a linear time-invariant response function from its magnitude. The Nose-to-Nose (NTN) calibration method can give the phase response of the equivalent sampling oscilloscopes, but the phase resolution can only achieve 250 MHz because the limit of the technology. In this study the fine phase response has been reconstructed. Although the truncation of the Kramers-Kronig transform using three basic functions may approximate gives rise to large errors in estimated phase, these errors may be approximated by using three basic functions. This result rests on data obtained by an NTN technique in combination with a swept-sine calibration procedure. The NTN technique yields magnitude and phase information over a broad bandwidth, yet has low frequency resolution. The swept-sine procedure returns only the magnitude of the oscilloscope response function, yet can be made at any frequency at which fundamental microwave power standards are available. As an example, we get the fine phase response of equivalent sampling oscilloscopes Agilent 86100 C from dc to 40 GHz; its frequency resolution achieves 1 MHz. In the process of this analysis, we observe that the true oscilloscope response function as measured by the NTN calibration is indistinguishable from the reconstructed phase response over a very large bandwidth. At last we analyze the phase uncertainty of the phase response, and the uncertainty analysis process is provided. The results show that the algorithm can be used to get the fine phase response of the equivalent sampling oscilloscopes.