Green Card for car insurance

The 'cross border card" has nothing to do with whether you have purchased CDW insurance or not. You need to request this cross border card when making a reservation, so you will be able to drive through borders. (I forgot to request it when booking a car in Croatia years ago; fortunately, my car already happened to have one, because it was the only car they had left!) At some borders, you will need to show it, to prove the car isn't say stolen. At tourist borders in Croatia at the Neum corridor (small slice of Bosnia north of Dubrovnik that juts out to the coast), you may not have it checked, but otherwise, crossing into Montenegro and Bosnia, mine was checked.

If you decline CDW insurance, then you are liable for damage to the car somehow. The car company will preauthorize a big deposit on the credit card when you pick up the car. If there's damage to the car when you bring it back, that's when the insurance comes into play. The cost of damages will go against your deposit, and you'll have to have that reimbursed.

I tried using my Amex card's "premium rental car insurance" coverage a few years ago while renting a car in Croatia. I thought I was covered - good thing, because I jumped a curb and seriously damaged my car (rented from Oryx) and needed to swap for another one. Unfortunately, the "Amex Assurance" company (insurance company Amex uses) either did not know how to talk to a little Croatian car company or didn't exert much effort to do so - because Oryx never responded to them after I made my claim. So Amex Assurance said, "sorry!" So I wound up paying over $600 USD in damages anyway. So much for the "insurance."

I had made my reservation through EconomyCarRentals, which included "excess" insurance on the car, thank goodness, so it was covered after a 800 euro deductible or something like that. Amex was supposed to cover everything else - but obviously, if they find some way to ignore your claim ("Hey, the company never replied to the letter we mailed them - wonder why, because we only charge them 20 euros as a service charge!"), what difference does it make?

Up to you if you want to risk using your credit card for the insurance. I will say that had I used a bigger car company like Hertz or Avis, Amex Assurance might have talked to them more easily. Then again, I would have paid 2X or more for the cost of the rental.

You need to tell the rental company all the countries where you plan to drive their car. Some may not allow certain border crossings or may not automatically include the correct paperwork. For instance, when I rented a car in Thessaloniki a few years ago, Avis Greece did not allow border crossings with the car they had and told me that a car with the proper paperwork would have to come from Athens and would cost about an extra thousand dollars for two weeks.

Also check the fine print on your credit card coverage to make sure it works in all of your destinations. Some countries are excluded, as well as some types of vehicle (such as large vans or luxury cars). Here's an example: https://usa.visa.com/support/consumer/card-benefits/consumer-auto-rental-collision-damage-waiver.html