  The full sky cosmic microwave background polarization field can be decomposed
into 'electric' and 'magnetic' components. Working in harmonic space we
construct window functions that allow clean separation of the electric and
magnetic modes from observations over only a portion of the sky. Our
construction is exact for azimuthally symmetric patches, but should continue to
perform well for arbitrary patches. From the window functions we obtain
variables that allow for robust estimation of the magnetic component without
risk of contamination from the probably much larger electric signal. For
isotropic, uncorrelated noise the variables have a very simple diagonal noise
correlation, and further analysis using them should be no harder than analysing
the temperature field. For an azimuthally-symmetric patch, such as that
obtained from survey missions when the galactic region is removed, the
exactly-separated variables are fast to compute allowing us to estimate the
magnetic signal that could be detected by the Planck satellite in the absence
of non-galactic foregrounds. We also discuss the sensitivity of future
experiments to tensor modes in the presence of a magnetic signal generated by
weak lensing, and give lossless methods for analysing the electric polarization
field in the case that the magnetic component is negligible.
