to justify (something) by using evidence or firm behaviour

insist, declare, maintain

to write one's name on the back of (a cheque)

support, authorize

to show that (a person, statement, act etc) is right, reasonable or proper

legitimize, substantiate

to make (something) stronger by adding or supplying more people or material

strengthen, augment

to give evidence; to be evidence of (something)

vouch for; give testimony

to be responsible for; express confidence, in a person, a person's character

give assurance

pledge, promise

pledge, promise