Well, since I wasn't just sitting around waiting, I did find one way of accomplishing this. In case you're interested:
http://www.1tehnicka.hr/estuff/books/0-672/0-672-30832-0/ch15.htm#E69E205 I found I can define a multi-column UNIQUE key by executing the following statement:
CREATE TABLE [dbo].[ContractInformation] (
[OwnerID] [int] NOT NULL,
[ClaimNumber] [varchar] (20) NOT NULL,
[ContractNetworkCode] [varchar] (3) NOT NULL,
[DateStamp] [datetime] NOT NULL ,
[SeqNum] [int] NULL ,
[NetworkCode] [varchar] (3) NULL ,
[Used] [varchar] (1) NULL ,
[DateSent] [datetime] NULL ,
[DateReceived] [datetime] NULL ,
[RepricedStatus] [int] NULL ,
[PPOBilledDate] [datetime] NULL ,
[PayerBilledDate] [datetime] NULL ,
[ReadyToBill] [varchar] (1) NULL ,
[ParticipatingPPO] [varchar] (1) NULL,
CONSTRAINT UK_OwnerID_ClaimNumber_ContractNetworkCode UNIQUE (OwnerID, ClaimNumber, ContractNetworkCode)
) ON [PRIMARY]
GO