The spectrum and morphology of the radio emission (similar to 0 degrees.5 extent) from MSH 15-52 (or G320.4-1.2) indicates that there is no association with the similar to 0 degrees.2 plerion of the 150 ms pulsar PSR B1509-58. The plerionic synchrotron spectrum is visible only in X-rays, and the steepening of the photon spectral index from similar to 1.6 below a few keV to similar to 2.1 above similar to 10 keV is consistent with a crossover from adiabatic losses to synchrotron losses in a plerionic field strength B similar to 8 x 10(-6) G. A similar field is derived from equipartition between field and particles. Synchrotron loss in such a weak field is small enough to explain why this plerion is similar to 20 times larger than the X-ray plerion of the Crab. Relativistic electrons in the similar to 0 degrees.2 source scatter 2.7 K MBR photons and possibly IR photons from surrounding dust grains to TeV energies, and the resulting inverse Compton photon spectrum is expected to be harder than epsilon(1)(-2) up to epsilon(1) similar to 20 TeV, with a softening above this energy. The gamma-ray flux is expected to exceed the Crab flux above epsilon(1) similar to 5 TeV. Nooitgedacht atmospheric Cherenkov TeV observations of MSH 15-52 reported here were not sensitive enough to constrain the field strength of the nebula, but future large zenith angle Cherenkov observations should be able to probe the spectrum at epsilon(1) much greater than 1 TeV, allowing a measurement of B.