  We present measurements of the low--temperature excess frequency noise of
four niobium superconducting coplanar waveguide microresonators, with center
strip widths $s_r$ ranging from 3 $\mu$m to 20 $\mu$m. For a fixed internal
power, we find that the frequency noise decreases rapidly with increasing
center strip width, scaling as $1/s_r^{1.6}$. We show that this geometrical
scaling is readily explained by a simple semi-empirical model which assumes a
surface distribution of independent two-level system fluctuators. These results
allow the resonator geometry to be optimized for minimum noise.
