Copy the serial output to a file (kermit, pyserial, screen, whatever). Write a program that reads that file and chops it up into individual "test case" results. Keep the test case results in memory or on disk, as appropriate.
Write a junit/testng test. Each test function will read one of the above test case results and evaluate it for correctness. This will generate a junit/testng test results xml file. Set up your jenkins config to look for the junit/testng results xml file.
