We study ionic transport in nano- and microcrystalline (1-x)Li(2)O:xB(2)O3 composites using standard impedance spectroscopy. In the nanocrystalline samples (average grain size of about 20 nm), the ionic conductivity sigma(dc) increases with increasing content x of B2O3 up to a maximum at x approximately 0.5. Above x approximately 0.92, sigma(dc) vanishes. By contrast, in the microcrystalline samples (grain size about 10 &mgr;m), sigma(dc) decreases monotonically with x and vanishes above x approximately 0. 55. We can explain this strikingly different behavior by a percolation model that assumes an enhanced conductivity at the interfaces between insulating and conducting phases in both materials and explicitly takes into account the different grain sizes.