Finding the results of a genius bar appointment?

You might want to open "My Support" (link below)

and sign in to see status of your case or repair.

My Support - Official Apple Support

(Am not sure whether or not the cost will be displayed.)

or

You can also check the status of a repair using the following link:

(you will need the repair ID and serial number)

Check your repair status - Apple

All the best :-)

Thank you for your reply, parks200.

Re: " I need a repair statement of what outcome we reached

I just got an estimate of how much it would cost".

Wondering how the estimate was delivered to you:

Eg: You might want to search for eMails from Apple around that date.

or

If you used the support app for the Genius Bar appointment, perhaps there's a communication / response / quote from there,

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Re: "I know the employees can look up the results".

As we are all Apple users, like yourself, in this community,

no-one here has access to anything other than their own Apple accounts.

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Re: Do you know if it is possible to get proof of the repair estimate without scheduling a new appointment and going to the store?

Sorry, I do not know of another way to obtain proof.

Perhaps you could try the employees at Mac Repair & Service - Apple Support

(ie: There's a "Contact us" link on that webpage.)

or for other devices:

Product Service and Repair Information - Official Apple Support