Continental rifts form by extension, and their subsequent evolution depends on the tectonic and climatic boundary conditions. We investigate how faulting, topography, and the evolution of the sediment flux during rifting are affected by these boundary conditions, in particular whether it is possible to correlate tectonic activity, topography, and sediment flux on long timescales (40 Myr). We use a thermomechanical model coupled with a landscape evolution model and present a series of 14 models, testing the sensitivity of the models to crustal strength, extension rate, and fluvial erodibility. The degree of strain localization drives the structural evolution of the modeled rifts: slow extension, high crustal strength, and efficient surface processes promote a high degree of strain localization, resulting in fewer active faults with larger offset. Overall, the magnitude of sediment production correlates with the degree of strain localization. In case of unchanged erosional power and similar amount of extension, systems with slower extension produce more sediment owing to a stronger positive feedback between erosion and fault offset. We observe a characteristic sequence of events, reflecting the morpho‐tectonic evolution of rifts: the highest rock uplift rates are observed before the maximum elevation, and the highest sediment flux postdates the peak in elevation. Our results indicate that for natural systems, the evolution of the sediment flux is a good proxy for the evolution of topography, and that a time lag of 2–5 Myr between the peaks in main tectonic activity and sediment flux can exist. Plain Language Summary: Continental rifting is the response of the uppermost part of the Earth to extensional, tectonic forces. The resulting landscape consists of subsided, sediment‐filled basins and uplifted, high‐elevation rift shoulders. Resolving what contributes to rifting on long‐timescales (i.e., tens of millions of years) from natural examples is challenging, since inverting the sedimentary record to resolve correlations between tectonic activity, topography, and the sediment production relies on several assumptions. We use computer models to simulate continental rifting, and subject the models to different boundary conditions. This allows us to have a holistic view of the rifting process under variable conditions over a 40‐million‐year period, and we assess how the topography, tectonic deformation, and sediment production evolve over time. We see that the degree of localization of deformation is decisive for the evolution of the rifts, and that localization correlates with sediment production. Furthermore, the temporal evolution of the sediment production reflects the tectonic and topographic evolution. Moving from models to natural examples, our findings indicate that the evolution of the sediment production is a good proxy for topography. However, a time lag of 2–5 million years could exist between the main tectonic activity and the highest sediment production. Key Points: Coupled, thermomechanical models show that during continental rifting, the sediment flux reflects the topographic evolution of riftsHigh crustal strength, slow extension, and efficient surface processes promote strain localization and sediment productionModel results suggest a time‐lag of 2–5 Myr between rifting and the peak in sediment flux [ABSTRACT FROM AUTHOR]