You can use any of the doThrow(),doAnswer(),doNothing(),doReturn() family of methods from Mockito framework to mock void methods(check out Mockito API docs)
For example,
Mockito.doThrow(new Exception()).when(instance).methodName();
or you may combine it with follow-up behavior,
Mockito.doThrow(new Exception()).doNothing().when(instance).methodName();
Presuming that you are looking at mocking the setter setState(String s) in the class World below is the code uses doAnswer method to mock the setState.
World mockWorld = mock(World.class);
doAnswer(new Answer<Void>() {
public Void answer(InvocationOnMock invocation) {
Object[] args = invocation.getArguments();
System.out.println("called with arguments: " + Arrays.toString(args));
return null;
}
}).when(mockWorld).setState(anyString());