What is stopping you importing the specific exception and using it in your with pytest.raises statement? Why is this not working? It would be more helpful if you could provide more detail about what problem you are facing.

# your code

class CustomError(Exception):
    pass


def foo():
    raise ValueError('everything is broken')

def bar():
    raise CustomError('still broken')    

#############    
# your test

import pytest
# import your module, or functions from it, incl. exception class    

def test_fooErrorHandling():
    with pytest.raises(ValueError) as excinfo:
        foo()
    assert excinfo.value.message == 'everything is broken'

def test_barSimpleErrorHandling():
    # don't care about the specific message
    with pytest.raises(CustomError):
        bar()

def test_barSpecificErrorHandling():
    # check the specific error message
    with pytest.raises(MyErr) as excinfo:
        bar()
    assert excinfo.value.message == 'oh no!'

def test_barWithoutImportingExceptionClass():
    # if for some reason you can't import the specific exception class,
    # catch it as generic and verify it's in the str(excinfo)
    with pytest.raises(Exception) as excinfo:
        bar()
    assert 'MyErr:' in str(excinfo)

pytest.raises(Exception) is what you need.

Code

import pytest

def test_passes():
    with pytest.raises(Exception) as e_info:
        x = 1 / 0

def test_passes_without_info():
    with pytest.raises(Exception):
        x = 1 / 0

def test_fails():
    with pytest.raises(Exception) as e_info:
        x = 1 / 1

def test_fails_without_info():
    with pytest.raises(Exception):
        x = 1 / 1

# Don't do this. Assertions are caught as exceptions.
def test_passes_but_should_not():
    try:
        x = 1 / 1
        assert False
    except Exception:
        assert True

# Even if the appropriate exception is caught, it is bad style,
# because the test result is less informative
# than it would be with pytest.raises(e)
# (it just says pass or fail.)

def test_passes_but_bad_style():
    try:
        x = 1 / 0
        assert False
    except ZeroDivisionError:
        assert True

def test_fails_but_bad_style():
    try:
        x = 1 / 1
        assert False
    except ZeroDivisionError:
        assert True

Output

============================================================================================= test session starts ==============================================================================================
platform linux2 -- Python 2.7.6 -- py-1.4.26 -- pytest-2.6.4
collected 7 items 

test.py ..FF..F

=================================================================================================== FAILURES ===================================================================================================
__________________________________________________________________________________________________ test_fails __________________________________________________________________________________________________

    def test_fails():
        with pytest.raises(Exception) as e_info:
>           x = 1 / 1
E           Failed: DID NOT RAISE

test.py:13: Failed
___________________________________________________________________________________________ test_fails_without_info ____________________________________________________________________________________________

    def test_fails_without_info():
        with pytest.raises(Exception):
>           x = 1 / 1
E           Failed: DID NOT RAISE

test.py:17: Failed
___________________________________________________________________________________________ test_fails_but_bad_style ___________________________________________________________________________________________

    def test_fails_but_bad_style():
        try:
            x = 1 / 1
>           assert False
E           assert False

test.py:43: AssertionError
====================================================================================== 3 failed, 4 passed in 0.02 seconds ======================================================================================

Note that e_info saves the exception object so you can extract details from it. For example, if you want to check the exception call stack or another nested exception inside.