Currently run-webkit-tests tracks per-test stderr output if it exists, and reports on it in the results file. The old Chromium run-webkit-tests would log stderr output to the log file, but not store it separately. The new-run-webkit-tests should probably follow the lead of run-webkit-tests. Alternatively we could concat stderr output onto stdout, which would cause the tests to fail, but this could lead to flaky test failures and/or harmless logging being treated as a failure.
*** This bug has been marked as a duplicate of bug 37739 ***