protected JSONObject myMethod(final String param1, final String param2)
{
…
}

final MyService mymock = Mockito.mock(MyService.class, Mockito.CALLS_REAL_METHODS);
    final String pararm1 = “param1”;
    Mockito.doReturn(myData).when(mymock).myMethod(param1, param2);

public class MyClass {
    protected String protectedMethod() {
        return "Can't touch this";
    }
    public String publicMethod() {
        return protectedMethod();
    }
}

@RunWith(MockitoJUnitRunner.class)
public class MyClassTest {

    class MyClassMock extends MyClass {
        @Override
        public String protectedFunction() {
            return "You can see me now!";
        }
    }

    @Mock
    MyClassMock myClass = mock(MyClassMock.class);

    @Test
    public void myClassPublicFunctionTest() {
        when(myClass.publicFunction()).thenCallRealMethod();
        when(myClass.protectedFunction()).thenReturn("jk!");
    }
}