Contact your city's hazardous waste facility. Inform the facility that you have asphalt emulsion that you need to dispose of. The facility will provide you with a specific location that accepts such materials for disposal. The material will be broken down if necessary or handled with the necessary steps to reuse it.
Transport your asphalt emulsion driveway pieces or containers of the emulsion sealer to the facility.
Provide the facility with proper identification if required. Most facilities require identification to prove you are a resident of the area under their jurisdiction if you wish to dispose of the materials free of charge.