A search is performed against word starts – and seeing your serial “number” format, this field is text. (In a number field, a search for 543941 would NOT find 5439410.)
Try using the = or == operator to match against the entire word (or field, depending on your data and intentions), like
Enter Find Mode
Set Field [ Table::serial ; "==" & SomeSerialNumber ]
I've tried your suggestion and I get "error 401". When I look on the layout in the field specified in
Set Field [ Table::serial ; "==" & SomeSerialNumber ] I find "==SomeSerialNumber". The == has been added to serial number which causes the find to fail.
Is there something else needed?