The answer to this question has two parts, because it was something I needed to think about a bit before I could answer. I'm including both answers I provided to this question because I think both are valid.
My initial response:
Personally, when I've underquoted, I've just treated it as a learning experience and make sure not to do it again and hold to that price for that job (but I obviously wouldn't offer that same price even to the same customer in the future.) I have never quoted something that is below my actual costs, so when I've made mistakes like this I've basically just spent time working for a lot less than I'm worth. The Paleo in Maine book from my presentation yesterday is an example of that.
My eventual response:
I spent some time thinking about it and talked to Jay and to one of my business mentors up here in Maine, and here's how I'd handle the situation if it happened to me in the future.
I'd still probably try to stick to my original quote if at all possible, but I would let them know that after reviewing exactly what work they'd need to be done that it would really cost $X. I'd tell them that I could do it at the price of the original quote but they really wouldn't get the quality product that they deserve. If I literally couldn't do it at that price, then I'd just have to tell them no, and if they raise a stink about it then it probably wasn't a customer I'd want to deal with anyway.
One thing to be careful about is to make sure that the person knows your actual price for what they're receiving. Even if I did do the job at the underquoted price, I'd still do as great a job as I could, but you don't want that person to brag about how cheap you are, you want them to talk about what great work you do. Make sure they understand that you won't be able to honor that price for other people so that they don't lead others to think you'd do work that cheaply for them.
This wasn't shared on the webinar as it had slipped my mind, but even though I stuck to my original quote with that Paleo in Maine book, he did actually give me a tip in his final check. I forget exactly how much it was without checking my records, but it was something on the order of an extra $50 or $100 which was a good percentage over what I'd charged him, even if it wasn't as much as I would have charged had I known what I was going to be doing for him or even had just started from a current quote and not one that was 6 months out of date.