Here's a revised version of your code which still works plus it illustrates how to raise a ValueError the way you want. By-the-way, I think find_last(), find_last_index(), or something simlar would be a more descriptive name for this function. Adding to the possible confusion is the fact that Python already has a container object method named __contains__() that does something a little different, membership-testing-wise.

def contains(char_string, char):
    largest_index = -1
    for i, ch in enumerate(char_string):
        if ch == char:
            largest_index = i
    if largest_index > -1:  # any found?
        return largest_index  # return index of last one
    else:
        raise ValueError('could not find {!r} in {!r}'.format(char, char_string))

print(contains('mississippi', 's'))  # -> 6
print(contains('bababa', 'k'))  # ->

Traceback (most recent call last):
  File "how-to-raise-a-valueerror.py", line 15, in <module>
    print(contains('bababa', 'k'))
  File "how-to-raise-a-valueerror.py", line 12, in contains
    raise ValueError('could not find {} in {}'.format(char, char_string))
ValueError: could not find 'k' in 'bababa'

Update — A substantially simpler way

Wow! Here's a much more concise version—essentially a one-liner—that is also likely faster because it reverses (via [::-1]) the string before doing a forward search through it for the first matching character and it does so using the fast built-in string index() method. With respect to your actual question, a nice little bonus convenience that comes with using index() is that it already raises a ValueError when the character substring isn't found, so nothing additional is required to make that happen.

Here it is along with a quick unit test:

def contains(char_string, char):
    #  Ending - 1 adjusts returned index to account for searching in reverse.
    return len(char_string) - char_string[::-1].index(char) - 1

print(contains('mississippi', 's'))  # -> 6
print(contains('bababa', 'k'))  # ->

Traceback (most recent call last):
  File "better-way-to-raise-a-valueerror.py", line 9, in <module>
    print(contains('bababa', 'k'))
  File "better-way-to-raise-a-valueerror", line 6, in contains
    return len(char_string) - char_string[::-1].index(char) - 1
ValueError: substring not found

You said it, ValueError is a specific Exception. A short example :

try:
    print int("hello world")
except ValueError:
    print "A short description for ValueError"

If you change "hello world" with an int, print int(42), you will not raise the exception.

You can see doc about exceptions here.