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Methods for measuring the absolute center-of-mass energy using dileptons frome$^{+}$e$^{-}$ collision events are further developed with an emphasis onaccelerator, detector, and physics limitations. We discuss two main estimators,the lepton momentum-based center-of-mass energy estimator, $\sqrt{s}_{p}$,discussed previously, and new estimators for the electron and positroncolliding beam energies, denoted $E^{\text{C}}_{-}$ and $E^{\text{C}}_{+}$. Inthis work we focus on the underlying limitations from beam energy spread,detector resolution, and the modeling of higher-order QED radiative correctionsassociated with photon emissions originating from initial-state-radiation(ISR), final-state-radiation (FSR), and their interference. We study theconsequent implications for the potential of these methods at center-of-massenergies ranging from 90 GeV to 1 TeV relevant to a number of potentialaccelerator realizations in the context of measurements of masses of the Z, W,H, top quark, and new particles. The statistical importance of the Bhabhachannel for Higgs factories is noted. Additional extensive work on improvingthe modeling of the luminosity spectrum including the use of copulas is alsoreported.

Further investigation of dilepton-based center-of-mass energy measurements at e$^{+}$e$^{-}$ colliders