What documents are necessary to perfect a loan secured with stock certificates? UCC? Security Agreement? Assignment of Certificates?

Stock certificate, stock power signed exactly like the stock certificate (one per stock certificate), security / pledge agreement.

That's if certificates have been issued. If you are taking an assignment of a brokerage account it would be handled differently.

Don't forget:

Regulation U-1, unless stocks are not margin or publicly traded.

Check the certificate to see if there are any restrictions printed on the certificate to restrict pledging or cashing them in. Some certificates could have restrictions placed on them and those would be denoted by a large stamp detailing the restriction.

Stock Certificates are possessory collateral (unless held in a brokerage account). UCC-1 not necessary.

I did forget about Reg U