It strongly depends upon what you want to coat onto Cu surface, maybe you need 3 steps, but the first 2 steps should be

1. degreasing (using an acidic and/or alkaline cleaner, depending upon what contamination are on your Cu surface, you may need to start with an alkaline cleaner, neutrallize, then acidic cleaner, then use DI water until neutral)

2. microetch (take some acidic persulfate solution and remove 1 micron of the Cu surface, then wash with DI water until neutral, then immediately apply your coating.

If still delamination, you may want to apply some silane coupling agent in a 3rd process step before coating.

May be you are working with MW. Impact modified epoxy resin is very good for it. It acceptable use nanoparticle in the coating to enhance cohesive strength also. 

If you are doing Sputtering.. check the stresses within the coatings..

As referred by Mr. Wessling, surface cleanliness is an important factor which shpuld be considered for adhesion Control..

Check als the thermal misfit between the coatimg and Substrate if you are depositing These films at high temperatures..

Please provide more information regarding your problem so that ist possible to find a clear solution for it.

My answer earlier is based on successfully coating on large copper net exposed to saline environment for quite long time without copper degradation, It does not interfere with electromagnetic radiation.

Maybe，you should try to prepare the coatings with argon shielding，which can avoid oxidation around the bond zone.

Primer (праймер - rus.) is needed for organic (polymer) coatings (after oxide removal). Onion or garlic juice is entry-level primer, more complex primers ask in next door supermaket.  

Nickel- and tin-plating  are the most available metallic anti-oxidation coatings for copper.

http://www.nwepaints.co.uk/acatalog/PrimersGalvanised.html

To: Andrei Rogoza:

Thank you very much for your advices, their clarity and completeness.

Best regards,           Leonid

To: Andrei Rogoza:

Thank you very much for your advices, their clarity and completeness.

Best regards,           Leonid

procedure 1:

- All surfaces must be degreased, detergent washed with 5% biprox or equivalent, high pressure (3000 PSI minimum) fresh water washed and allowed to dry.

- All degreased surfaces shall be treated with generous brushing or spraying with the etchant solution. After allowing the etchant to react (2 minutes), the surface shall be

thoroughly rinsed with clean fresh water.

Procedure 2:

- Alternatively, light abrasive blasting can be used utilizing fine grade abrasives.

- Before the application of any coating the prepared surface shall be checked for soluble salts contamination.

Coating spalling occurs in four modes

Both critical peak temperatures and spalling mode depended on the type of coating system

The contributions made to your question so far will all help to improve the adhesion of your coating material to metallic copper surface. Don't forget you're trying to fight the most difficult problem, the adhesion of organic material -coating resin, which is essentially hydrophobic of which electrons are strongly bound to their nuclei- onto a material -copper of which electrons gather to make a cloud which move around- and these two materials are extremely incompatible. The problem will always persist whether the interaction of copper surface is with an undercoat or primer or whatever. Besides to all recommendations done so far I can add two more things:

1. Etch the copper surface to create cavities which improve mechanical locking of coating material.

2. Treat the surface with surface active agents containing sulfur or amino groups. The copper is very prone to interact  with such compounds, as both sulfur and nitrogen behave as electron deficient atoms. Essentially most metal surfaces exhibit similar behavior. The hydrophobic end of such surface active compounds will be involved in cohesive interactions with the resin of the coating material.