When generating test script (menu iTools | Generate Test Script ...) it is possible to select saving of report from script in JUnit format from testIDEA dialog. This format is recognized by Jenkins server, which can then include testIDEA test results to its reports.
IMPORTANT: If Jenkins server is run as a Windows service, then it is not started under normal user account, and ConnectionMgr::connectMRU() call in Python script can not locate the last winIDEA started. There exist two solutions to avoid this problem:
iconnectDllPath = 'C:/winIDEA/2012/iConnect.dll'
To use test results in Rational DOORS from IBM, export results in CSV format, with CSV header checkbox checked. The first line in CSV file will contain column headers, which will become attribute names after import to DOORS. Then you can link requirements to test results - the links can be based on testIDEA's test ID.