Photostable polymeric tandem dyes are provided. The photostable polymeric tandem dyes include a water soluble light harvesting multichromophore and a luminescent metal complex covalently linked to the multichromophore and in energy-receiving proximity therewith. Also provided are labelled specific binding members that include the subject dyes. Methods of evaluating a sample for the presence of a target analyte and methods of labelling a target molecule in which the subject polymeric tandem dyes find use are also provided. Systems and kits for practicing the subject methods are also provided.