In this paper, we explore the power of the cosmic microwave background (CMB) polarization (Emode) data to corroborate four potential anomalies in CMB temperature data: the lack of large angular-scale correlations, the alignment of the quadrupole and octupole (Q-O), the point-parity asymmetry, and the hemispherical power asymmetry. We use CMB simulations with noise representative of three experiments -the Planck satellite, the Cosmology Large Angular Scale Surveyor (CLASS), and the LiteBIRD satellite -to test how current and future data constrain the anomalies. We find the correlation coefficients ρ between temperature and E-mode estimators to be less than 0.1, except for the point-parity asymmetry (ρ = 0.17 for cosmic-variance-limited simulations), confirming that E-modes provide a check on the anomalies that is largely independent of temperature data. Compared to Planck component-separated CMB data (SMICA), the putative LiteBIRD survey would reduce errors on E-mode anomaly estimators by factors of ∼ 3 for hemispherical power asymmetry and point-parity asymmetry, and by ∼ 26 for lack of large-scale correlation. The improvement in Q-O alignment is not obvious due to large cosmic variance, but we found the ability to pin down the estimator value will be improved by a factor 100. Improvements with CLASS are intermediate to these.