We measure coronal magnetic field strengths of 1750 G at a height of 8000 km above a large sunspot in NOAA AR 10652 at the west solar limb on 2004 July 29 using coordinated observations with the Very Large Array, the Transition Region and Coronal Explorer, and three instruments (CDS, EIT, MDI) aboard the Solar and Heliospheric Observatory. This observation is the first time that coronal radio brightness temperatures have been analyzed in a 15 GHz solar radio source projected above the limb. Observations at 8 GHz yield coronal magnetic field strengths of 960 G at a height of 12,000 km. The field strength measurements combine to yield a magnetic scale height LB=6900 km. The radio brightness temperature maxima are located away from a sunspot plume that appears bright in EUV line emission formed at temperatures around several ×105 K. We use the density-sensitive emission-line intensity ratio of O IV 625.8 Å/554.5 Å to derive an electron density ne (in units of cm-3) of logne=10.1+/-0.2 at the base of the plume.