  We have investigated both the temperature and the power dependence of
microwave losses for various dielectrics commonly used as substrates for the
growth of High critical Temperature Superconductor thin films. We present
measurement of niobium superconducting $\lambda/2$ coplanar waveguide
resonators, fabricated on $La_{0.3}Sr_{0.7}Al_{0.65}Ta_{0.35}O_3$ (LSAT), $MgO$
(MgO) and $LaAlO_3$ (LAO), at the millikelvin temperature range and at low
input power. By comparing our results with the Two-Level System (TLS) model, we
have discriminated among different dominant loss mechanisms. LSAT has shown the
best results as regards the dielectric losses in the investigated regimes.
