Li-7 solid State NMR has been used to characterize lithium aluminium titanium phosphate and lithium lanthanum titanate ceramics. Both materials have high ionic mobilities at room temperature and this is reflected in their static Li-7 powder patterns. In the case of the phosphate based ceramic, a narrow Lorentzian peak is observed above 300 K, which narrows further with increasing temperature. The accompanying quadrupolar structure, with C-Q (quadrupolar coupling constant) similar to 40 kHz, suggests that the lithium ions are hopping rapidly between equivalent, high electric field gradient sites. The Al-27 and P-31 magic angle spinning (MAS) spectra reveal an asymmetric phosphorus peak and two distinct aluminium resonances. The room temperature powder pattern of Li0.33La0.57TiO3 shows a dipolar broadened peak which narrows quite suddenly at 310 K revealing quadrupolar satellites with C-Q similar to 900 Hz. A second lithium site is also observed in this material, as indicated by a further, weaker quadrupolar structure (C-Q similar to 40 kHz).