  We review the observations of supernova remnants (SNRs) and pulsar-wind
nebulae (PWNe) that give information on the strength and orientation of
magnetic fields. Radio polarimetry gives the degree of order of magnetic
fields, and the orientation of the ordered component. Many young shell
supernova remnants show evidence for synchrotron X-ray emission. The spatial
analysis of this emission suggests that magnetic fields are amplified by one to
two orders of magnitude in strong shocks. Detection of several remnants in TeV
gamma rays implies a lower limit on the magnetic-field strength (or a
measurement, if the emission process is inverse-Compton upscattering of cosmic
microwave background photons). Upper limits to GeV emission similarly provide
lower limits on magnetic-field strengths. In the historical shell remnants,
lower limits on B range from 25 to 1000 microGauss. Two remnants show
variability of synchrotron X-ray emission with a timescale of years. If this
timescale is the electron-acceleration or radiative loss timescale, magnetic
fields of order 1 mG are also implied. In pulsar-wind nebulae, equipartition
arguments and dynamical modeling can be used to infer magnetic-field strengths
anywhere from about 5 microGauss to 1 mG. Polarized fractions are considerably
higher than in SNRs, ranging to 50 or 60% in some cases; magnetic-field
geometries often suggest a toroidal structure around the pulsar, but this is
not universal. Viewing-angle effects undoubtedly play a role. MHD models of
radio emission in shell SNRs show that different orientations of upstream
magnetic field, and different assumptions about electron acceleration, predict
different radio morphology. In the remnant of SN 1006, such comparisons imply a
magnetic-field orientation connecting the bright limbs, with a non-negligible
gradient of its strength across the remnant.
