Q:

Differentiate ø and ae

When I do an SQL ae and æ are interpreted as the same (danish collation):
select * from directories where path='test.dk\kkl$\Faelles'

Is there anyway to do a query that handles æ and ae as unique?

A:

I used exactly @Heinzi's code here (he used the collation)
I just wanted to show how you can use it in a WHERE clause and in ORDER BY clause with a sample 
At first I though you require NVARCHAR() data type but I see VARCHAR() also support Danish characters without an issue ( at least your sample )
declare @code nvarchar(100) = 'æ'
--declare @code nvarchar(100) = 'ae'

select * 
from Danish
where code = @code COLLATE Danish_Greenlandic_100_CI_AI 
--order by code COLLATE Danish_Greenlandic_100_CI_AI desc

So you need to set the Collation with COLLATE clause in WHERE clause or in ORDER BY for each condition or group by field,
After @Thomas' comment, I added following query.
It will produce seperate rows for 'æ' and 'ae'
SELECT
    path COLLATE Danish_Greenlandic_100_CI_AI, 
    migrate, ismigrationroot, 
    COUNT(*) as CNT 
FROM directories 
GROUP BY 
    path COLLATE Danish_Greenlandic_100_CI_AI,
    migrate,
    ismigrationroot 
HAVING 
    COUNT(*) > 1 and 
    ismigrationroot is not null

