A basic methodology for earthquake early warning is the use of point‐source models fed with observational data from triggered stations. The 2011 Off the Pacific Coast of Tohoku earthquake in Japan ( 9.0) (the Tohoku‐Oki earthquake) and its aftershock and induced earthquake activity, however, highlighted the following technical challenges of point‐source models: (1) underprediction of the strong motion of large earthquakes with finite faults, (2) missing earthquakes during intense seismic activities, and (3) overprediction of the strong motion of multiple simultaneous earthquakes. We propose the propagation of local undamped motion (PLUM) method to address these technical challenges. The PLUM method is a simple wavefield‐estimation approach that predicts seismic intensities directly from observed real‐time seismic intensities near target sites. The PLUM method can outperform point‐source‐model approaches in terms of (a) accurate ground‐motion prediction for large earthquakes with finite faults and (b) robust event declaration for complex earthquake sequences. On the other hand, available warning times provided by the PLUM method are not expected to be very long. We also introduce a hybrid method that uses both the PLUM method and a point‐source‐model approach to maximize the total available warning times and avoid missing strong motion. When applied to the Tohoku‐Oki earthquake ( 9.0), the PLUM and hybrid methods predicted accurate strong motion without underestimation and provided sufficient warning times in most areas. For the subsequent earthquake sequence after the 9.0 earthquake, the PLUM method robustly detected and processed large earthquakes despite considerable intense seismicity. A statistical analysis using large aftershocks and induced earthquakes demonstrated that the PLUM and hybrid methods predicted strong motion more accurately than the point‐source‐model approach of the Japan Meteorological Agency. These findings indicate that the PLUM and hybrid methods can be effective countermeasures to address the technical challenges faced by point‐source models.