flights to Denmark in July

Wouldn't you prefer to fly non stop?
SAS (legacy carrier Scandinavian Airline) has non stops from the USA to Oslo and Copenhagen.

A non stop flight is always nicer than having to change somewhere. But if you're going to change somewhere, it's always nice to avoid London.

But what does your plan look like? If you're going to Norway, my first suggestion would not be to fly to Denmark.

Where are you departing from? I’ve done non-stop ORD to CPH multiple times. Last year, went on to Oslo after several days in Copenhagen.

I think those of us reading your question do not understand your itinerary and “must sees”, timeframes, cost, etc. so are confused.

What is your point of origin, and what seating class do you intend to buy?

Going on a cruise originating in Copenhagen, is my guess for the explanation of the 'oddity' of destination(s)

For what it’s worth, this past September (I know, not July), we flew Denver>London Heathrow>Copenhagen. We were using British Airways frequent flyer Avios points, so that was a major factor in deciding which route. We flew straight to Copenhagen, after flying straight to London from Denver.

After a few days in Copenhagen, we flew Norwegian Air (budget fare) from Copenhagen to Trondheim, Norway, up the western coast of that country. After several weeks touring Norway, we flew Norwegian again, from Oslo to Copenhagen for another couple of days. The flight home was Copenhagen to London to Denver, again, For what it’s worth. Enjoy your trip!

When we traveled to Denmark and then on to Norway we did a connection in Iceland. The Reykjavik airport is incredibly smaller than either London or Amsterdam We live in the Boston area so flew Boston to Reykjavik then connected to another flight to go to Copenhagen. Also, Iceland does have some promotions sometimes about tacking on a day or two to your layover to visit the country. We didn't do this but might be an idea for you. Our return trip home was Bergen to Reykjavik then connected to another flight to Boston.

I would try and avoid London or Amsterdam airports if possible as those are notoriously busy and I personally would be too stressed worry about delays, strikes (these were going on at Amsterdam airport I believe the summer of my trip to Denmark/Norway), etc. The Iceland airport is just easier to navigate because of it's size.

Agree to Badger.

If you want to travel to Bergen have a look at Bergen airport which international airports in Europe can be reached by direct flights:
https://avinor.no/en/airport/bergen-airport/

We will be taking a Windstar cruise that departs from Denmark, up the coast of Norway and
then disembarks in Scotland. Yes I prefer a direct flight but always interested in what others
suggest.

SAS is starting a non-stop Atlanta - Copenhagen flight on June 17th.

https://community.ricksteves.com/travel-forum/transportation/sas-non-stop-atlanta-copenhagen-flight-starts-june-17th

I don't wish to rain on anyone's parade here, but SAS were unquestionably the most unenjoyable international flights I've ever taken. Unfriendly, unhelpful and argumentative flight attendants (with one lone exception), shoddy equipment and atrocious EuroBusiness service (I had a middle seat for a 3-hour flight). Never again.

American Airlines will have nonstop service from Philadelphia to Copenhagen starting 6/6/24. I'm not sure where you are located in the U.S. but that might be an option to consider.

I flew TATL on SAS: 11+ hours from LAX to CPH. I also took a 3-hour flight (Eurobusiness) from CPH to Malaga, Spain. Both flights were in my opinion unacceptable for a business class fare.

I booked the American airlines flight from RDU to Philadelphia and direct flight from Philadelphia to Copenhagen and return Copenhagen direct to Philadelphia and back to RDU.
I booked this flight months ago.
So the direct Philadelphia to Copenhagen has been available for some time.

The American flight from PHL to Copenhagen would be perfect! Thank you!!