Regardless of using unique constraint or unique index, the field can accept null values, however the uniqueness will result in only accepting a single row with null value.
The solution to allow nulls in unique fields is create a unique filtered index excluding the nulls of the index, due to that the uniqueness of the nulls will not be validated and multiple rows with nulls will be accepted.
Click through for the code. I enjoy asking this as an interview question. It’s a non-trivial problem with a non-trivial solution and isn’t a trick question.