Here are the quote and proof.
Here is the quote and proof.
Thank you for your help.
Note that you'll hear native speakers use "Here's" (the contraction of "here is") but you shouldn't hear the two separate words "Here is". If two separated words are used then, in your context, it should be "Here are". Note that I would expect your sentence to read "Here are the quote and the/some proof".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.