Yes, varicaps are good and there are even varicaps with very large capacitance swings exactly for this purpose.
But it does require a very steady voltage and many more parts than just a single passive to not accidentally load the resonant circuit to the point that it becomes ineffective. You need to de-couple considerably to make this work, especially without injecting (phase) noise. And frequency stability and phase noise can be extremely annoying in particular applications.
But it does require a very steady voltage and many more parts than just a single passive to not accidentally load the resonant circuit to the point that it becomes ineffective. You need to de-couple considerably to make this work, especially without injecting (phase) noise. And frequency stability and phase noise can be extremely annoying in particular applications.