Intimidation is fear wrapped in razor blades
To fight fear and intimidation, work to get out of your own way and increase your knowledge.
Fear is an internal response. It's driven by a view of the world/situation and anticipated negative outcomes.
Intimidation is fear plus a perceived, active external threat.
I fear what might be lurking just outside that door. I'm intimidated by the wolf staring right at me.
How does one deal with these natural human responses?
We no longer live in hunter-gatherer times. I’d bet a lot of first world fear is real, but grounded in misunderstanding. Is the CEO really that intimidating, or have you been unable to get to know her yet? The experience of meeting her could your knowledge increase knowledge. Either a) she's not that scary, or b) she is that scary but now you've learned more about what works out doesn't work in communicating with her.
To fight fear and intimidation, work to get out of your own way and increase your knowledge.