  We compute the local spectrum of the magnetic field near a metallic
microstructure at finite temperature. Our main focus is on deviations from a
plane-layered geometry for which we review the main properties. Arbitrary
geometries are handled with the help of numerical calculations based on surface
integral equations. The magnetic noise shows a significant polarization
anisotropy above flat wires with finite lateral width, in stark contrast to an
infinitely wide wire. Within the limits of a two-dimensional setting, our
results provide accurate estimates for loss and dephasing rates in so-called
`atom chip traps' based on metallic wires. A simple approximation based on the
incoherent summation of local current elements gives qualitative agreement with
the numerics, but fails to describe current correlations among neighboring
objects.
