  We propose a scheme for quantum estimation by means of parametric
amplification in circuit Quantum Electrodynamics. The modulation of a SQUID
interrupting a superconducting waveguide transforms an initial thermal two-mode
squeezed state in such a way that the new state is sensitive to the features of
the parametric amplifier. We find the optimal initial parameters which maximize
the Quantum Fisher Information. In order to achieve a large number of
independent measurements we propose to use an array of non-interacting
resonators. We show that the combination of both large QFI and large number of
measurements enables -in principle- the use of this setup for Quantum Metrology
applications.
