We study the effect of salt concentration on the ionic conductance and translocation of single DNA molecules through nanocapillaries made out of quartz glass. DNA translocation experiments were performed in aqueous solution for concentrations of KCl between 10 mM and 2 M while ion conductance was characterized from 1 mM to 2 M KCl concentration. Here, we develop a model for the conductance of conical nanocapillaries taking into consideration the surface charge of the quartz glass. We demonstrate that the conductance of our nanocapillaries shows similar behavior to silicon oxide nanopores at low and high KCl concentrations. Finally, we show that DNA translocations in high KCl concentrations (400 mM–2 M) cause a reduction in the ionic current. In contrast, DNA translocations at low KCl concentrations (10–300 mM) lead to increases in the ionic current. Our new results, which until now have not been shown for nanocapillaries, can be well understood with an adapted model.