Drying a microelectronic topography. At least some of the illustrative embodiments are methods that include placing a microelectronic topography inside a process chamber, providing a non-aqueous liquid to the process chamber until at least 90% of the volume of the process chamber contains the non-aqueous liquid, pressurizing the process chamber by way of a fluid different than the non-aqueous liquid, ceasing activity with respect to the process chamber until the non-aqueous liquid and fluid form a mixture that is substantially homogenous, venting the process chamber while simultaneously providing the fluid to the process chamber, and venting the process chamber in a manner which prevents formation of liquid in the process chamber.