There are several reasons vehicles encounter NOx failures. If this particular Honda Civic is equipped (check your Honda's underhood emissions label for the abbreviation "EGR") with an EGR system we'd recommend beginning by inspecting the EGR system components first.
The EGR valve is responsible for re-circulating a small amount of exhaust gas back into the combustion chamber. This is done to cool down the chamber temperature by producing an inert gas along with the regular fuel mixture. Nitrous Oxides emissions are formed when engine chamber temperatures rise above 2500* F. Keeping the chamber cool reduces NOx emission. The EGR valve should be inspected to ensure it is operating properly. A working EGR valve should be able to open its passage using manifold vacuum.
If your 1996 Honda Civic is a non-EGR equipped model your focus should be on proper fuel control (Air/Fuel Mixture), vacuum leaks which could create lean fuel conditions, and the catalytic converter.
Weak engine cooling and high cylinder compression will cause high NOx as well in both non-EGR and EGR valve equipped Honda Civics.
Engine Cooling - If your engine's cooling system is not working efficiently, chances are there is an excessive amount of NOx being created. Remember NOx (Nitrous Oxides) is created only when an engine's combustion chamber temperatures reach over 2500F. A bad cooling system will create NOx.
High Cylinder Compression - Carbon build-up within your engine's combustion chambers will cause increased engine temperature and high NOx. Carbon build-up normally develops in an engine's combustion chambers over some period of time. High increase in carbon build-up causes increased cylinder compression, which causes high temperatures, which result in high NOx emissions.
