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Over the last few years several groups have fabricated High Temperature Superconducting (HTS) thin film microwave devices which have included a ferroelectric thin film layer in their design. The electric field dependence of the ferroelectric promises desirable in-situ tuning of the frequency response. Here we present the results of our experiments on the tuning of a coplanar HTS resonator using single crystal strontium titanate (STO). We have patterned a simple coplanar resonator device onto Y-Ba-Cu-O thin films deposited on  magnesium oxide substrates. Careful consideration of the size, position and biasing of these high permittivity STO crystals with respect to the planar device allows us to minimise the perturbance to the plain resonators response whilst at the same time maximising the degree to which we are able to tune the device. We have also performed a series of capacitance measurements on our STO crystals to obtain reliable data for the dependence of the permittivity on temperature, applied bias and crystallographic orientation.