I'm a little ahead of you, and started the process as part of my retirement plan, sold off the two '68 GTXs, one word of mouth, one through this site. Came out in good shape financially, wouldn't have gone as well if an heir was trying to liquidate them. My daughter was interested in Baby Blue for about a month after I got the car back in 2013. When she lost interest I started making plans to pass it outside the family. Offered it to friends first, at a steep discount from book, when they passed on it, I sold the car for book value to a guy who had been after it for years.
The current GTX posed a bit of a dilemma, with a combination of relatively high market value, and strong sentimental attachment. For any newbies who don't know the story, I test drove the "Demonstrator" when the car was new, and I was 16. Bought it 52 years later, in near concours condition. My wife and I recently came to an agreement on disposal. We are on the short list to enter an upscale old folks home. No inside storage there, she won't pay for outside storage. I am fortunate to have a close friend, 15 years younger, with ample storage, financial means, and mechanical skills. Only downside is he's a Ford guy, likes the car, but doesn't love it.
He's agreed to take the car when I leave my house, if I'm still alive. If I predecease my wife, she sells it to him for a price the three of us have agreed on. He then gives the grandson of the original owner right of first refusal at that price. If no deal happens, he sells it as he sees fit. If my wife predeceases me, he continues to keep the car, and I pass the title to him as a gift.
My will also directs my executor on a procedure to liquidate the car in the unlikely event of the simultaneous death of me and my wife. As I retired attorney, I've covered all bases.