In this article, we report a method to damp microfluidic hydrodynamic fluctuations caused by flow sources. We demonstrate that compliance of elastomeric off-chip tubings can be used to damp fluctuations and lead to steady flow rates. We analyze the whole microfluidic system using electrical circuit analogies, and demonstrate that off-chip compliances are significant, especially for displacement pump driven systems. We apply this hydrodynamic damping method to microfluidic droplet generation. Our results show that highly monodisperse microdroplets can be obtained by syringe pump driven systems utilizing this damping effect. We reached a coefficient of variation of 0.39% for the microdroplet area using a standard T-junction geometry. Additionally, we demonstrated that pressure pumps inherently use this effect, and have so far led the high performances reported in the literature in terms of droplet monodispersity. The presented off-chip hydrodynamic damping method is not only low-cost and practical, but can also be used in elastomeric and rigid microchannels without need to introduce additional components to the fluidic circuit.