Many EMI and SI problems are related with a combination of inductance and capacitance without losses.
The effectiveness of different materials for shielding can be tested using near field probes and your vector network analyzer (VNA).
If your EMI filter is failing in high frequencies, check the frequency response of the components: parasitics limit the filtering effectiveness.
For many applications, especially in digital designs, you can see decoupling networks composed of several different (big and small) capacitors in parallel. But, sometimes this technique can be dangerous.
You can minimize your EMI/EMC and SI/PI problems by working as slow as possible. This is very well known advice from many experts, books, and seminars: you can minimize or solve electromagnetic interference (emissions/susceptibility) and signal or power integrity problems working as slow as possible.
Discover the eye diagram, a very useful visual tool to analyze the quality of your connections in digital and high frequency applications.
Sometimes a ferrite is used to remove ringing in some applications as in power electronics or digital circuits.
When designing an EMI/EMC filter the orientation relative to source and victim is critical for high effectiveness. Can you save components in your filters?
If you are a novice designer of electronic circuits, this is one of the best pieces of advice I can give you from my experience in EMI troubleshooting and training.
Take time to check for EMI, efficiency, temperature, safety, immunity, or any other requirement in your product.