The present invention provides an acidic aqueous polishing composition suitable for polishing a silicon nitride-containing substrate in a chemical-mechanical polishing (CMP) process. The composition, at point of use, comprises about 0.01 to about 2 percent by weight of a particulate calcined ceria abrasive, about 10 to about 1000 ppm of at least one cationic polymer, optionally, about 10 to about 2000 ppm of a polyoxyalkylene polymer; and an aqueous carrier therefor. The at least one cationic polymer is selected from a poly(vinylpyridine) polymer and a combination of a poly(vinylpyridine) polymer and a quaternary ammonium-substituted polymer. Methods of polishing substrates and of selectively removing silicon nitride from a substrate in preference to removal of polysilicon using the compositions are also provided.