  We report magnetic field dependent magnetization and microwave impedance
measurements on a MgB2 superconductor prepared by high pressure synthesis. We
find that the upper critical field is linearly dependent on temperature near Tc
and the dc irreversibility field exponent is ~1.4. The microwave data display
an excess surface resistance below Tc which is neither observed in low Tc nor
in high temperature superconductors (HTSC). The real part of the complex
conductivity, sigma1, shows a huge maximum below Tc and the imaginary part,
sigma2, is linear for temperatures less than 20 K, which can not be simply
accounted for by the weak coupling BCS model with an s-wave superconducting
order parameter. We speculate that this may be due to the two gaps reported by
other studies. Unlike measurements on the high temperature superconducting
cuprates, we find no evidence of weak-links in the superconducting state. By
inverting the magnetic field dependent impedance data, we find a vortex
depinning frequency that decreases with increasing magnetic field and evidence
for an anisotropic upper critical magnetic field.
