De la documentación de Python (http://docs.python.org/library/unittest.html):

import unittest

class WidgetTestCase(unittest.TestCase):
    def setUp(self):
        self.widget = Widget('The widget')

    def tearDown(self):
        self.widget.dispose()
        self.widget = None

    def test_default_size(self):
        self.assertEqual(self.widget.size(), (50,50),
                         'incorrect default size')

    def test_resize(self):
        self.widget.resize(100,150)
        self.assertEqual(self.widget.size(), (100,150),
                         'wrong size after resize')

Aquí está, cómo invocar esos casos de prueba:

def suite():
    suite = unittest.TestSuite()
    suite.addTest(WidgetTestCase('test_default_size'))
    suite.addTest(WidgetTestCase('test_resize'))
    return suite

¿Es posible insertar el parámetro custom_parameter en WidgetTestCase como:

class WidgetTestCase(unittest.TestCase):
    def setUp(self,custom_parameter):
        self.widget = Widget('The widget')
        self.custom_parameter=custom_parameter

?