Rossby wave trains triggered by tropical convection strongly affect the atmospheric circulation in the extratropics. Using daily gridded observational and reanalysis data, we demonstrate that a technique based on linear response theory effectively captures the linear response in 250-hPa geopotential height anomalies in the Northern Hemisphere, using examples of step-like changes in precipitation over selected tropical areas during boreal winter. Application of this method to six Coupled Model Intercomparison Project Phase 5 (CMIP5) models, using the same tropical forcing, reveals a large intermodel spread in the linear response, associated with intermodel differences in Rossby wave guide structure. The technique is then applied to a projected tropics-wide precipitation change in the HadGEM2-ES model during 2025-2045 DJF, a period corresponding to a 2°C rise in the mean global temperature under the RCP8.5 scenario. The response is found to depend on whether the mean state underlying the technique is calculated using observations, the present-day simulation, or the future projection; indeed, the bias in extratropical response to tropical precipitation because of errors in the basic state is much larger than the projected change in extratropical circulation itself. We therefore propose the linear step response method as a semi-empirical method of making near-term future projections of the extratropical circulation, which should assist in quantifying uncertainty in such projections.