Due to their ease of fabrication and mechanical flexibility, silver nanowire transparent electrodes have been touted as a promising replacement for metal oxides such as indium tin oxide (ITO). Here we study an additional advantage: their high transparency in the near-infrared region (NIR) which is highly desirable for some applications. For electrodes that are 96% transparent in the visible, ones made from ITO are only 35% transparent at a wavelength of 2500 nm, but those made from silver nanowires maintain a transparency as high as 94%. Experiments and modelling show that to minimize the transparency drop from the visible to the NIR, the nanowires should be sparse and larger in diameter. This is found to be attributed to both the larger average spacing between nanowires in such networks and the lower absoprtion losses of larger diameter nanowires in the NIR.