Proof of the reliability or credibility of someone can come from vetting that person.
Prior to becoming the candidate's supporters, they made sure she had been vetted by people who had dealings with her in the past.
Or, for example, you could ask a person you want to know you can trust,
Have you been vetted by your past employers?
Would you mind if I vetted you by calling your former employers?
In a similar vein, you could ask the person who says he is trustworthy,
Can you vouch for your reliability?
Can Mrs. Overstreet vouch for you?
In other words, you are asking if the person can prove his or her reliability, thus giving you assurances he or she will do what was promised.
You could also approach another person who knows the person you are vetting and ask him or her,
Can you vouch for Sarah's reliability? Has she ever made promises to you she didn't keep?
Or, in wording which is probably archaic,
Are you willing to vouchsafe Sarah's trustworthiness to us?
Say your father, for example, were to cosign a loan for you he could say to the loan officer,
I'll be happy to vouchsafe the loan for my daughter.
To Become Surety
A little off the mark, but somewhat related, is the concept of surety. One of the quickest ways of giving proof to someone that you trust them is by co-signing on a loan they are taking out.
Becoming surety for a stranger or for someone you do not really know that well, however, is asking for trouble. You are foolish to cosign a loan without proof that a person is reliable, trustworthy, and faithful.
The third party in the above scenario could be a bank. The bank wants assurances the borrower has someone as a back-up should the borrower default on the loan. Perhaps the borrower has not yet established credit and needs someone to cosign a loan, thus becoming surety for both the borrower and the bank. Sometimes the borrower's credit is a little spotty. Interestingly, the word surety is related etymologically to the word assurance, meaning proof which gives peace of mind to someone. A bank officer, for example, might ask you,
Are you willing to become surety for Mr. Williams, in the event he defaults on this loan?
The Earnest and The Deposit
Another evidence or proof of a person's sincerity is the earnest. We do not use the word very much today, favoring the phrase "down payment." The earnest, or down payment is a form of proof that you can trust the person who, for example, wants to buy something from you but cannot come up with all the money right away. The buyer will give you some earnest money to show good faith that he or she is definitely interested in purchasing your item.
Another word for earnest is deposit. Under some circumstances, if the contract specifies it, a deposit is not refundable. If for whatever reason (and the reasons are specified in the contract, whether verbal or written) the person does not follow up the deposit by paying the balance due, well, tough noogies.