Hilbert's 16th problem asks to classify the isotopy types of real algebraic hypersurfaces in projective space. In the 1980s Viro developed patchworking as a method to construct real algebraic hypersurfaces with unsually large mod 2 Betti numbers. Interpreted within the larger framework of tropical geometry, patchworking leads to a combinatorial approach to real tropical hypersurfaces. We report on a recent implementation of this method in polymake, we compare with a previous implementation of de Wolff et al. in Sage, and we report on experiments with surfaces of degrees up to 6.