It is possible to move a resonance by adding metal on the inside, or to reduce or eliminate it by adding absorber. Be careful with absorbing matrial if you are working with power or low loss is important. Also, out gassing can be a problem long term in some applications. You want to be sure actual circuit operation is boring, not exciting!
Both absorber and extra metal can be less effective than you might think, depending on the mode you are trying to modify. Some modes have most of their energy concentrated in the dielectric. Do whatever you like in the air and it doesn't care. Those kinds of modes can be real hair-pullers.
Not all circuits are affected by all resonant modes. Best thing to do is to analyze some kind of representation of your circuit in the actual box size. If you see a suck-out at a known resonant frequency, you know you have problems.
If your top cover gets real close to the circuit, it will modify your circuit performance. If you take that route, be sure to do shielded EM analysis and compensate the design.
If you just say to heck with it, and leave the cover off, the resonance will (probably) dissappear, but you will get radiation. If there are other components around that can couple out of, or into your circuit, there will be problems. In fact, one way to do a quick check on radiation is to do an unshielded EM analysis (Momentum, IE3D, Ensemble), followed by a shielded analysis (Sonnet, EMSight) and see if there is any significant difference.
If it is a pure rectangular box, you are best using a shielded planar EM analaysis like our own Sonnet. You can include absorber easily by specifying a lossy dielectric layer. Chunks of metal can be included as well, but that starts to use up memory and analysis time. At some level of complexity, you would want to switch over to a volume mesher to see what happens when the lid goes on. We work a lot with CST here (support and sales in North America) and I would recommend CST for this application. The broad band high resolution frequency domain data you get from a time domain analysis like CST is really good when searching for narrow high-Q resonances.
As I mentioned above, if you want a quick list of resonant frequencies, download SonnetLite htt://www.sonnetsoftware.com, enter your box and dielectric geometry and click Analysis->Estimate Box Resonances.
Even if there are no resonances, many microwave engineers (including me) have had the joy of seeing a beautiful amplifier response on the ANA, then when we put the cover on, it becomes a beautiful oscilator. Use your circuit analysis tools, combined with planar EM analysis of the passive portion of your circuit (use internal ports for connecting your transistor) and look at stability factor...with the cover on.