What you’re trying to convey may probably be expressed with “d’une certaine façon”. Originally it means “in a certain, specific way” which is also the literal meaning of “somehow”. Both in French and in English the meaning is often extented, as you describe, toward “in some unknown, unexpected way”.

“En quelque sorte” was however the first idea that came to mind and I believe it’s a good translation of “somehow” in many other contexts. Also, you could translate the particular usage of “somehow” from the title of this question by “d’une certaine manière” which gives a little more importance to the method, the chosen way of doing things.

Someone in a WordReference Forum proposed en quelque sorte. There’s a lot of discussion there about how to translate “somehow” so you might want to have a look.

Well, first let me say that the example you provided:

He somehow managed to say goodbye.

doesn’t strictly convey the meaning*:

‘that was nearly incredible, because although it happened I have no idea how it happened’

But one can always say:

Contre toute attente, il a réussi à me dire au revoir.

I don’t know if that is exactly what you are looking for but Larousse and Wikipedia say that the expression denotes a retourenement de situation inattendu. You were not expecting this to happen and yet it DID.

The first example returned by linguee is:

[…] fierté parmi tous les citoyens de la zone euro quant à la manière dont nous avons procédé, peut-être contre toute attente.

The english for that is:

It could ensure that all citizens in euro land are proud of the way it has been done, maybe against all expectations.

Which I don’t know if you would be comfortable rephrasing into:

It could ensure that all citizens in euro land are, somehow, proud of the way it has been done.

Note that applying this expression to your first example would give us something like:

Vous m’avez, contre toute attente, donné une bonne idée.

Which can sound like you were not expecting such a good idea from your interlocutor.

*at least that’s how it sounds to me