score:5
For this trip, you would not need to do anything at Newark besides proceed to your gate. This will likely mean taking a shuttle bus to Terminal B, where SAS operates. Do not exit the secure area, but take the airside bus, which will bring you near the gate for your flight to Copenhagen. There is no exit passport check in the US.
At Copenhagen, you will need to go through immigration control. This is because both Copenhagen and Sweden are part of the Schengen area, so they are treated as one "country" for immigration purposes. When you arrive in Copenhagen, you'll walk to the Schengen part of the airport and wait in line for passport control and a security check. As a non-EU/EEA/Swiss citizen, this may take some time.
SAS considers 45 minutes to be the minimum connection time in this case. This means that it should at least be possible in an hour, but you won't have much margin for delays, either if your flight is late or there are lines at the airport You may be more comfortable with a longer connection.
If you have purchased a single airline ticket, the airline will ultimately be responsible for rebooking you on another flight at no charge if you can't make your connection. However, this may significantly delay your travel plans depending on when the next flight leaves. I would certainly not do this with multiple tickets.
As far as customs is concerned, you will do this in Stockholm. If you've purchased a single ticket, your bags will be automatically transferred in Newark and Copenhagen. You'll claim your checked bags in Stockholm. Unless you are bring special goods with you or are bringing valuable items that you will leave behind in the EU, you can just walk out through the "nothing to declare" area.
Upvote:3
If you need to book this as multiple tickets: this will NOT work. Don't do this.
If you can book it on a single ticket than the airline is responsible for getting you there, if your miss your connection. According to their statistics you have a good change to making this otherwise they wouldn't sell you the ticket.
Best option would be to take the SAS direct flight from EWR<->ARN (and skip CPH). That's currently offered from around $1050 round trip (ALB<->ARN through EWR, May, midweek).