I have activated a coupon called "Free shipping", and marked the option "Free shipping". But this coupon withdraws the discount before the shipping is added already in the basket, and therefor it doesn´t withdraw anything. After the basket, in the checkout, the shipping is added, and this discount coupon is pointless.
Have I misunderstood anything about the free shipping coupon?

Just mark the products you want as free shipping

You should must marked the product that you want to detect the discount amount. If this issue is still not get resolved then please contact your shooing cart manufacturer.
 
Any more question would be much appreciated.