If you're wanting to find This:
CID34000 Shaynet 1000000
But not this:
CID34000 Shaynet 34000
Then you'll want to do something like this:
Select InterfaceAlias, CircuitID
FROM Interfaces
Where CircuitID is not null
AND Patindex('%' + CircuitID + '%' ,InterfaceAlias) = 0
You may need to cast/convert CircuitID depending on datatype....
You can also add other clauses to narrow down your search at your preference such as:
AND InterfaceAlias LIKE '%CID% (from your original query)