I use CST often, and used it for helical resonators, specifically the Eigenmode solver. The latest version should do an eigenmode analysis with open boundaries, which you’d need for coils. My resonator was in a cavity.
Diodes exhibit capacitance that varies with respect to their DC bias. I know this is used in GHz RF applications.
Using opamps to create virtual reactive components (capacitors, or inductors) that would otherwise be impractical to build directly (too high of value) is an interesting trick.
Peregrine makes several digitally tunable capacitors (switched capacitor banks) that work to S-band and can handle moderate power. I have used them for antenna tuning.
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