Copenhagen to Stockholm (the direct trains) is best booked on sj.se.

Domestic trains in Denmark don't need a reservation.

Trains in Norway are best booked by phone via Entur (add +47 for Norway). The reservations will be emailed; reservations with a 1st class pass are free of charge in Norway.

If that doesn't work for you, then please mention route, date and departure time for any train you'd like to book.

Hi in Denmark almost all trains are reservation optional.

In Sweden only SJ Intercity, SJ X2 high speed, Snalltoget and all long distance trains like nighttrains. You can book the reservation via sj.se for SJ trains or the website of the train operator like Snalltoget or VY.

In Norway best way ist to call EnTur Call Center, you get the reservation via email/SMS.

On the 25th of January Swedish SJ released tickets until the 28th of May. However around Easter and Ascension about 40 % of the tickets aren’t released as there is uncertainty around construction works.

If you have problems with making reservations for specific trains, please give details here and you will get advice.

Thank you for those responses. So I have a First Class pass and I want to book a reservation on March 22nd for the 14.21 departure from Copenhagen to Stockholm. I just need a seat reservation since I have a pass. If I go to the Sweden Rail website https://www.sj.se/ they appear to just have full price tickets -s there a way to just get a reservation and not buy a full price ticket?

You put your Eurail Pass as discount so you pay only the reservation. If you have a Mobile Pass you can get here 

Not as a discount but as SJ prio when you add the traveller, see pictures below.

You pay 62 SEK for a seat when you have an Interrail/Eurail pass. 

In 1st class it's a bit more, SEK 143 :)

You have all been very helpful. Thank you.

Pity the Swedish Rail website has been attacked by Anonymous Sudan. It’s down

It should be accessible via a VPN connection:

This is honestly the most ridiculous system for ticketing. I couldn’t imagine it becoming more complicated, but it does. I was making some seat reservations to Bergen from Oslo for another leg of the trip and the reservations were going to on paper and mailed to my address in the United States. No other options. Shaking my head in disbelief.

I refer to my first answer above: call Entur. Or use their chat (I read reports that booking also works that way). They will send reservations via email.