Enhanced liquid water flows through carbon nanotubes reinvigorated the study of moisture permeation through membranes and micro- and nano-channels. The study of water vapour through micro-and nano-channels has been neglected even though water vapour is as important as liquid water for industry, especially for encapsulation of electronic devices. Here we measure moisture flow rates in silica microchannels and interdiffusive water vapour flows in anodic aluminium oxide (AAO) membrane channels for the first time. We construct theory for the flow rates of the dominant modes of water transport through four previously defined standard configurations and benchmark it against our new measurements. The findings show that measurements of leak behaviour made using other molecules, such as helium, are not reliable. Single phase water vapour flow is overestimated by a helium measurement, while Washburn or capillary flow is underestimated or for all channels when boundary slip applies, to an extent that depends on the slip length for the liquid phase flows.