Few geomagnetic ground observations exist of the Earth's strongest core field anomaly, the South Atlantic Anomaly (SAA). The geomagnetic repeat station on the island Tristan da Cunha, located half-way between South Africa and South America at 37?? 05' S, 12?? 18' W, is therefore of crucial importance. We have conducted several sets of repeat station measurements during magnetically quiet conditions (Kp 2o or less) in 2004. The procedures are described and the results are compared to those from earlier campaigns and to the predictions of various global field models. Features of the local crustal bias field and the solar quiet daily variation are discussed. We also evaluate the benefit of continuous magnetic field recordings from Tristan da Cunha, and argue that such a data set is a very valuable addition to geomagnetic satellite data. Recently, funds were set up to establish and operate a magnetometer station on Tristan da Cunha during the Swarm magnetic satellite mission (2011-2014).