We report on spectropolarimetric observations across the Mg II h and k lines at 2800 Å made by the Ultraviolet Spectrometer and Polarimeter on board the Solar Maximum Mission satellite. Our analysis confirms the strong linear polarization in the wings of both lines observed near the limb, as previously reported, but also demonstrates the presence of a negatively (i.e., radially oriented) polarized signal between the two lines. We find evidence for fluctuations of the polarization pattern over a broad spectral range, resulting in some depolarization with respect to the pure scattering case when observed at very low spatial and temporal resolutions. This is consistent with recent theoretical modeling that predicts this to be the result of redistribution effects, quantum interference between the atomic levels of the upper term, and magneto-optical effects. A first attempt at a quantitative exploitation of these signals for the diagnosis of magnetic fields in the chromosphere is attempted. In active regions, we present observations of circular polarization dominated by the Zeeman effect. We are able to constrain the magnetic field strength in the upper active chromosphere using an analysis based on the magnetograph formula, as justified by theoretical modeling. We inferred a significantly strong magnetic field (̃500 G) at the 2.5σ level on an exceptionally active, flaring region.