A promising approach to reconstruct oceanographic scenarios of past time slices is to drive numerical ocean circulation models with sea surface temperatures, salinities, and ice distributions derived from sediment core data. Set up properly, this combination of boundary conditions provided by the data and physical constraints represented by the model can yield physically consistent sets of three-dimensional water mass distribution and circulation patterns. This idea is not only promising but dangerous, too. Numerical models cannot be fed directly with data from single core locations distributed unevenly and, as it is the common case, scarcely in space. Conversely, most models require forcing data sets on a regular grid with no missing points, and some method of interpolation between punctual source data and model grid has to be employed. An ideal gridding scheme must retain as much of the information present in the sediment core data while generating as few artifacts in the interpolated field as possible. Based on a set of oxygen isotope ratios, we discuss several standard interpolation strategies, namely nearest neighbour schemes, bicubic splines, Delaunay triangulation, and ordinary and indicator kriging. We assess the gridded fields with regard to their physical consistence and their implications for the oceanic circulation.