  The complex dielectric constant $\hat{\epsilon} = \epsilon_1 + i \epsilon_2$
of SrTiO$_3$ reaches high values $\epsilon_1 \approx 2*10^{4}$ at cryogenic
temperatures, while the dielectric losses ($\epsilon_2$) are much stronger than
for other crystalline dielectrics. SrTiO$_3$ is a common substrate for oxide
thin films, like the superconducting LaAlO$_3$/SrTiO$_3$ system, but the large
$\epsilon_1$ and $\epsilon_2$ restrict high-frequency quantum devices on
SrTiO$_3$. Here we present superconducting coplanar Nb resonators on SrTiO$_3$,
which we successfully operate in a distant-flip-chip geometry at frequencies
that exceed 1 GHz. We find a pronounced and unexpected increase in resonator
quality factor $Q$ at temperatures below 1 K, reaching up to $Q \approx 800$.
We attribute this to substantial changes of the dielectric losses in SrTiO$_3$
at mK temperatures, and we also detect non-monotonous changes in the
temperature-dependent $\epsilon_1$. These findings challenge our present
understanding of the dielectric properties of SrTiO$_3$ and at the same time
demonstrate that cryogenic high-frequency devices on SrTiO$_3$ are more
feasible than previously assumed.
