Train from Stockholm to Copenhagen

We have travel through out Europe and my answer will probably surprise you. The cost of airfare on some of the cheaper carriers is so competitively priced that you might want to consider going by plane. Norway has a very competitively priced economy airline as well as more well known Ryan Air. There are a lot of these low priced flights connecting the cities of Europe.

About 5 hours on direct trains about every 2 hours. Prices as low as $25 eq if you go out 4 weeks.
https://www.sj.se/travel/booklowprice.form?l=en&l=en&intcmp=1173732

I suggest flying on SAS. SAS includes one bag and airports in Scandinavia are a breeze. When I got to Copenhagen I took the metro into town and it was fast and easy. There was a long line to buy train tickets in the arrivals hall, so I walked past to the metro and sure enough there were three more ticket machines closer to the metro and no line.

I don't know of any ferries between Stockholm and Copenhagen.

The train is about 5 hours. If your travel date is flexible, use the best buy calendar on the SJ site to find lower priced days:
https://www.sj.se/travel/booklowprice.form?l=en&l=en&intcmp=1173732

The plane can be cheaper, depending on when you buy and your date of travel, but make sure you factor in the cost of getting to Arlanda when you compare prices.

It's 409 miles between the two cities. I'd suggest flying between them on a budget European air carrier--like Norwegian Air Shuttle.

I think you need to decide if you want to see scenery along the way or just get to Copenhagen. I prefer scenery and would take the 5 hour train. It is a pleasant, clean, train and you can refer a seat in a quiet car or not depending upon your preference. To me, for this length of train ride, a flight is a waste of time and less comfortable than the train. That's just me. You need to decide which your prefer. Wray