We had a lovely 2 night stay at Mathiaes' apartment. The location absolutely cannot be beat! Copenhagen is a pedestrian's paradise, the only time we used any transportation other than our feet was to take the metro to and from the airport.
Mathiaes was a fantastic communicator, replying within an hour (usually minutes!). We had flight delays and he was able to cheerily coordinate our late night check-in.
The apartment is lovely, and we will gladly stay again and highly recommend it to our friends. As other reviews have noted, the stairs are a bit steep and narrow. The space is a 3rd floor walk up, so I would not recommend it if you have loads of luggage or any mobility issues.