Uberspace is the best Option, you just need your own Domain.

Edit: I'll add an explanation. Uberspace ist a german hoster. It follows a pay what you want model (minimum: 1€) and practices data avoidance. For example, you can open an account and test it for a month, and then send money for that account to keep him, but you are never asked for your name.

I just use it for mails right now, but I could also host a webpage or something there. It's a full server.

The mailsystem has a nicely working roundcube-webinterface, one can of course also use IMAP. Without a custom domain the mailadress will look not very nice (but still work), but supporting a custom domain is very easy. It should ideally stay with a different domain registrar.

The whole administration interface is great - minimal on the webpage (though many things are possible to do there), and everything more complicated works via ssh.

Just buy a domain and a small hosting plan that includes mail. I am using that setup for close to 10 years now and it is fantastic. I use all-inkl (hit me for my affiliate link if you want to sign up so I become rich) which are a high quality yet very affordable german host.

It's not in the EU (Switzerland), but https://mykolab.com/

As was already said, any webhosting package with email will do. Here is a selection of hosters in Germany that I find have a clean website an pricing structure and therefore feel less cheap and more trustworthy to me.

Hetzner: One of the bigger provider for hosting in Germany. They have their own datacenters in Bavaria. Manitu: Smaller, they also have their own datacenter. schokokeks.org: Small service run by a few techies. I'm sure there are a few of this type, I just happen to know somebody who is very happy with them.

Posteo.de [1] is decent, but they don't allow you to use your own domain. The recently launched mailbox.org [2] seems to be alright as well.

[1] https://posteo.de

[2] https://mailbox.org

MyKolab. As secure as a hosted service can get, located in Switzerland.

I'm using EUMX.net with large mailboxes and no problems so far. They seem to be quite a small company although very helpful when responding to email which they do with 24 hours.