How can I create a SQL unique constraint based on 2 columns?

I have a Table like this one:

|UserId   |  ContactID |  ContactName 
---------------------------------------
| 12456   |  Ax759     |  Joe Smith
| 12456   |  Ax760     |  Mary Smith
| 12458   |  Ax739     |  Carl Lewis
| 12460   |  Ax759     |  Chuck Norris
| 12460   |  Bx759     |  Bruce Lee

I need to add a constraint to this table so that no user can have duplicate contact id's. The users are importing data from various external systems so ContactId will not be unique across the board but will be unique on a per user basis.

I know how to create Unique and Non-Null contraints based on single columns but how can I create a unique contraints across 2 columns?

You can try this:

CREATE UNIQUE CLUSTERED INDEX index_name ON TABLE (col1,col2)

or

CREATE UNIQUE NONCLUSTERED INDEX index_name ON TABLE (col1,col2)

or

ALTER TABLE [dbo].[TABLE] ADD CONSTRAINT
    UNIQUE_Table UNIQUE CLUSTERED
    (
       col1,
       col2
    ) ON [PRIMARY]

You can add unique constraint tou your fields:

ALTER TABLE YourTable
ADD CONSTRAINT UQ_UserId_ContactID UNIQUE(UserId, ContactID)

You can try ALTER TABLE [TABLE_NAME] ADD UNIQUE (column1,column2,column3 ...columnN).

Hope this helps cheers.

CREATE TABLE [LineItems](
	[ID] [int] IDENTITY(1,1) NOT NULL,
	[OrderID] [int] NOT NULL,
	[LineItemNumber] [int] NOT NULL,
 CONSTRAINT [PK_LineItems] PRIMARY KEY CLUSTERED 
(
	[ID] ASC
),
 CONSTRAINT [UC_LineItems] UNIQUE NONCLUSTERED 
(
	[OrderID] ASC,
	[LineItemNumber] ASC
)
)

Here is the syntax for creating a unique CONSTRAINT as opposed to a unique INDEX.

ALTER TABLE publishers 
  ADD CONSTRAINT uqc_pub_name 
  UNIQUE (pub_name)

It is important to note that there are subtle differences dependent on which method you use to enfore the uniqueness of a column.

See the following MSDN reference for an interesting walkthrough of these:

http://msdn.microsoft.com/en-us/library/aa224827(SQL.80).aspx