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We describe a thin-film superconducting Nb microwave resonator, tunable towithin 0.3 ppm of the hyperfine splitting of $^{87}$Rb at $f_{Rb}=6.834683$GHz. We coarsely tuned the resonator using electron-beam lithography,decreasing the resonance frequency from 6.8637 GHz to 6.8278 GHz. For \emph{insitu} fine tuning at 15 mK, the resonator inductance was varied using apiezoelectric stage to move a superconducting pin above the resonator. We founda maximum frequency shift of about 8.7 kHz per 60-nm piezoelectric step and atuning range of 18 MHz.

Thin-film superconducting resonator tunable to the ground-state hyperfine splitting of $^{87}$Rb