  In this paper, we study tropicalisations of families of curves with a
singularity in a fixed point. The tropicalisation of such a family is a linear
tropical variety. We describe its maximal dimensional cones using results about
linear tropical varieties from Ardila and Klivans and from Feichtner and
Sturmfels. We show that a singularity tropicalises either to a vertex of higher
valence or of higher multiplicity, or to an edge of higher weight. We then
classify maximal dimensional types of singular tropical curves. For those, the
singularity is either a crossing of two edges, or a 3-valent vertex of
multiplicity 3, or a point on an edge of weight 2 whose distances to the
neighbouring vertices satisfy a certain metric condition. We also study
algebraic preimages of our singular tropical curves.
