We present ab initio transport calculations for molecular junctions that include graphene as a protecting layer between a single molecule and gold electrodes. This vertical setup has recently gained significant interest in experiment for the design of particularly stable and reproducible devices. We observe that the signals from the molecule in the electronic transmission are overlayed by the signatures of the graphene sheet, thus raising the need for a reinterpretation of the transmission. On the other hand, we see that our results are stable with respect to various defects in the graphene. For weakly physiosorbed molecules, no signs of interaction with the graphene are evident, so the transport properties are determined by offresonant tunnelling between the gold leads across an extended structure that includes the molecule itself and the additional graphene layer. Compared with pure gold electrodes, calculated conductances are about one order of magnitude lower due to the increased tunnelling distance. Relative differences upon changing the end group and the length of the molecule on the other hand, are similar.