Let's say you are the Danes, seeking to control the danish trade (mission) that has a goal of controlling 3 major ports in the baltic: Neva (Novgorod at 1444) Danzig (Teutonic order at 1444) and Lúbeck (Lúbeck at 1444)
You get Casus belli for these major ports, it's recommended to take Danzig and Neva first due to them being threatend by the regional powers, Muscovy and Poland-Lithuania.
However Lúbeck is tricky, since it's a part of the HRE, if you declare right away on them, the emperor aids them (Austria often keeps the 2nd election)
(in this guide i use Hamburg as an example but pretty much any nation will do, i did Hamburg due to Lúbeck being under my flag already)

As you can see, if i DoW on Hamburg, the emperor aids him.

So as you saw the emperor aids him if i DoW straight on Hamburg, but wait! There is a good chance a minor outside the empire allied him, like Riga.
If you have some luck, Riga (doesn't have to be Riga but it's an option) is allied to some minors in the HRE. In this case he was.
Once you notice that a member has an ally outside the empire, fabricate a claim or any other way to DoW, (im not sure here) do not co-belligerent the person you want to annex (the emperor may come in, correct me if im wrong)

(not Hamburg but Lúbeck) I annexed Lúbeck this way.

The emperor will ask you to give back territory, unlawful.
Just click no and get the penalty