Using catch-exception library, recommended way is to use the builder pattern:
import com.google.common.base.Supplier; // Google Guava
Supplier<MyClass> builder = new Supplier<MyClass>() {
   @Override
    public MyClass get() {
       return new MyClass();
   }
};
verifyException(builder).get();
If you are using JUnit 4 for unit testing, you can use Expected Exceptions:
public class TestClass {  
    @Test(expected = MyException.class)  
    public void createObjectTest() {  
        MyClass object = new MyClass();  
    }  
}  
In older version of JUnit youd simply catch your exception:
public class TestClass {  
    @Test  
    public void createObjectTest() {  
        try {  
            MyClass obj = new MyClass();  
            fail("An exception should be thrown!");  
        } catch (MyException e) { 
        }  
    }  
}