Acceptance of large bills in Denmark

In my experience, 200 kr bills are not at all unusual and shouldn't give you any issues (unless you're buying something very cheap, like less than 20 kr, from a very small store). The 500 kr bill is more unusual, but it should be fine in larger stores and restaurants. Some smaller stores and restaurants may refuse them.

The other answers already mention that breaking bigger notes in Denmark is not really a problem. But you can likely avoid getting big notes in the first place.

If you exchange the money in the country where it is the currency you can ask and should be given smaller notes. If not all, at least enough that you are not immediately stuck.
When you exchange money in your home country you will have less options when you ask for a certain kind of notes. You will then have to take what they have or leave without exchanging.

But check the cost of exchanging against using a card in the ATM and against using your card in shops and restaurants.
Using your card is often cheaper than traveling with cash and it has much less risk of losing all to pick pockets.

There are tricks to get money out of the ATM without getting too big notes.
Like going to a machine where you can select the notes they deliver. And asking for an amount which is smaller than the big note you want to avoid. Or at least select an amount which means that you do not only get big notes, like 1900 instead of 2000, so you can be sure not to get just 500 or 1000 notes. (Adjust numbers to what you actually need.) And most ATM do not give notes that will be too big.

It is getting less and less common to pay cash at all in all Scandinavian countries, so you may be given a strange glance no matter which bill you choose to pay with. Except for that, I wouldn't expect any problems paying with larger bills.

I moved to Denmark 7 years ago. As many people comment, cash is not all that common here anymore. Many are suggesting to skip cash all together, and just use a credit card. There are two reasons why that might not be the best idea. Danish establishments normally charge a percentage fee for foreign cards. Expect this to be up to 3%. Many smaller shops also do not accept standard foreign card types at all, only the danish standard DanKort. This made my life hard from time to time, as I could not get one until I had lived here for 2-3 years.

I have never been refused to pay cash any place in Denmark. Admittedly, I do not do it often anymore. If you bring 200kr bills, you will most likely not be refused anywhere. And 500 will work in absolutely the majority of cases as well.

So do not blindly rely on using foreign cards. At least some cash is a good idea.