On‐surface metal‐organic coordination provides a promising way for synthesizing different two‐dimensional lattice structures that have been predicted to possess exotic electronic properties. Using scanning tunneling microscopy (STM) and spectroscopy (STS), we studied the supramolecular self‐assembly of 9,10‐dicyanoanthracene (DCA) molecules on the Au(111) surface. Close‐packed islands of DCA molecules and Au‐DCA metal‐organic coordination structures coexist on the Au(111) surface. Ordered DCA3Au2 metal‐organic networks have a structure combining a honeycomb lattice of Au atoms with a kagome lattice of DCA molecules. Low‐temperature STS experiments demonstrate the presence of a delocalized electronic state containing contributions from both the gold atom states and the lowest unoccupied molecular orbital of the DCA molecules. These findings are important for the future search of topological phases in metal‐organic networks combining honeycomb and kagome lattices with strong spin‐orbit coupling in heavy metal atoms.