  We describe a thin-film superconducting Nb microwave resonator, tunable to
within 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{in
situ} fine tuning at 15 mK, the resonator inductance was varied using a
piezoelectric stage to move a superconducting pin above the resonator. We found
a maximum frequency shift of about 8.7 kHz per 60-nm piezoelectric step and a
tuning range of 18 MHz.
