CREATE DATABASE TestUC;
GO

USE TestUC;
GO

SELECT * INTO dbo.AllDBs1
FROM sys.DATABASES;

SELECT * INTO dbo.AllDBs2
FROM sys.DATABASES;
GO

CREATE UNIQUE INDEX UQ_AllDBs1 ON dbo.AllDBs1(database_id);

ALTER TABLE dbo.AllDBs2 ADD CONSTRAINT UQ_AllDBs2 UNIQUE (database_id);
GO

SELECT Name, is_unique_constraint
FROM sys.indexes
WHERE object_id IN (object_id(N'dbo.AllDBs1'), object_id(N'dbo.AllDBs2'))
AND is_unique = 1;

SELECT *
FROM sys.key_constraints
WHERE parent_object_id IN (object_id(N'dbo.AllDBs1'), object_id(N'dbo.AllDBs2'));