The effect of electron irradiation-induced shrinking on glass nanocapillaries with diameters ranging from 75 to 14 nm was analyzed by measuring the conductance characteristics with and without DNA translocation. We have investigated nanocapillary shrinking with a scanning electron microscope from several perspectives to understand the geometry of the shrunken nanocapillary. On the basis of this observation, the conductance was modeled with respect to the nanocapillary diameter, which allowed reproducing the experimental results. We then translocated DNA through the shrunken nanocapillaries and measured higher conductance drops for smaller diameters, reaching 1.7 nS for the 14 nm diameter nanocapillary. A model taking into account the conical shape of the shrunken nanocapillaries also supported this dependence. Next, we calculated the noise in the form of the standard deviation of the ionic conductance (between 0.04 and 0.15 nS) to calculate a signal-to-noise ratio (SNR) and compared it with nanopores embedded in 20 nm thick silicon nitride membranes. This shows that although nanocapillaries have smaller signal amplitudes due to their conical shape, they benefit from a lower noise. The glass nanocapillaries have a good SNR of about 25 compared with the SNR of 15 for smaller sized nanopores in silicon nitride membranes. The ability to use a modified model of nanopores to mimic the block conductance by DNA translocation provides a theoretical framework to support experimental results from translocating polymers such as DNA.