For general reference use the BBC World Average conditions. Very good guide.
Here's stuff on Copenhagen:
March Average max/min = +5/-1; Record max/min +19/-18
April Average max/min = +10/+3; Record max/min +22/-9
Check 5 day local forecasts 1 week before leaving:
It's a fun city for sure :)
Fondest memory: Canal ride admiring the chic buildings all around.
The sweet mermaid site.
You will find a normaly very reliable 6 days weather forecast at this link to the danish meteorologycal institut.
Or if you like it just for Copenhagen and in english
http://www.dmi.dk makes the official weather forecasts for Denmark. Some of the website is in english, and here you can read the forecast for different parts of Denmark. There is also a forecast for Copenhagen, here is a direct link: http://www.dmi.dk/eng/index/forecasts/forecast_for_copenhagen_and_zealand.htm
Fondest memory: If you instead chooses the tab "Danmark" at the top, you get to see a map with icons showing the weater forecast, and if you chooses "regionaludsigter" in the left column, you get different parts of Denmark.
Fondest memory: Ok for the most part the weather durring the summer has been great but make sure that you pack an umbrella or a raincoat.The weather can change on you in a moment!! I personally would always take a raincoat. There is usually quite a breeze here being on the coast and all. So you could look pretty funny trying to wrestle around with your umbrella in the wind.
Fondest memory: When I was in Copenhagen, I had the (mis)fortune to have a very unstable weather, changing every half hour between brilliant sunshine and rain. However, this provided unusual light perfect for photography, aking the colours stand out. So, do not despair if the weather looks grim, take your camera, put a good waterproof jacket on and step outside.