I need to look up a UCC filing for the state of California by the serial number of a machine, however I've not been successful at finding a resource to allow me to do so thus far. The UCC Connect that the state provides does not appear to offer serial number searches and other services I've seen do not appear to have this option either.

Any help would be much appreciated!!!

You probably won't find a resource for searching by serial number in UCC filings. The standard national UCC form does not have a field dedicated to "serial number", it only has a "collateral description" field. The UCC sites for most states only allow search by Debtor Name, Filing Number or Secured Party Name.