Hi there,
Apart from looking for a serious and stable company, which is obvious, I wouldn't look for much more than a fair price and a fair attitude in a European rep. As an illustrative parameter, you can simply count the number of pages on the contract...

Just like with all other shopping - get several quotes to get some feeling for the market, then choose the one that feels right. Assuming your own company's conduct is fair, there's not too much to the EU rep. issue anyway.
If I may quote a nice NB auditor fellow, he said that EU reps are there only for the case that something bad happens and the authotities needed to put their hands on somebody... that's why they are required to have their place of business inside the EU. Whether or not the rep. has insurance or not doesn't really change the big picture, apart from making the service a little more expensive for you. I am not aware of a specific legal requirement for such insurance, but of course it doesn't say that there isn't one in place.
As for thr price - most reps I know charge a one-time annual fee up front. I'm not too updated but a couple of years ago a 1-1.5K Euro PA would be considered fair. Some charge more, some less, but this was the ballpark figure.
Cheers,
Ronen.
When deciding on a European Authorized Representative what would you be looking for in the company?
Should the European Authorized Representative (Company) have insurance or any protection for performing the role?
Also what is an average fee for a European Authorized Representative, either a yearly fee or a month fee?
Thanks in Advance