The routes and time schedules for the North Zealand bus tours were established 50 years ago, when most American tourists had never seen the inside of a castle before. However, very few Danes lived in castles and compared with English, Scottish and French castles the Danish castles are not that fantastic. 
Unfortunately most limousine chauffeurs who do a North Zealand tour simply follow in the tracks of the busses. But: by using a limousine you avoid going by bus and you have a little more time at the different castles. 

The chauffeurs of V.I.P. Limousine Service try to do more than just "follow the busses".
If the weather permits, the tour can, for example, start by going via Lyngby and the old Lyngby Village to my favorite museum: Frilandsmuseet - The Open Land Museum.  Lyngby is located only 8 miles north of Copenhagen but going down Hovedgaden ("Main  Street")  you get an idea of what a typical Danish provincial town looks like.
The church in Lyngby is typical for the more than 1100 churches built in Denmark between 1100 and 1200: they were built on hills where the vikings had been praying to the old Nordic goods Odin and Thor - so that further prayers to those old gods were not possible.
The Lyngby Village is unique. In Lyngby the new town was built next to the old village instead of on top of it - so the old village is intact with many typical half-timbered houses and houses with thatched roofs.
Frilandsmuseet (Open Land  Museum)  was founded more than 100 years ago as a division of the National Museum.
Old, typical  farmhouses from all parts of Denmark have, over the years,  been  moved to the Museum where they have been painstakingly reconstructed. What makes the museum unique is that the farmhouses are fully furnished the way they were more than 100 years ago, so it is possible to get a very good idea of  what life was like for the more than 90% of the population living on farms at the time. For many that life was pretty rough!!
(You can now click here, get a clickable map of the museum - and see many of the houses.)
After spending an hour seeing a selection of typical houses at the Open Land Museum, the tour will probably go north, round the beautiful Sjælsø (Sjael-Lake) and through the forest to Hillerød and Frederiksborg Castle. The chauffeur will take you through the Castle which houses the National Historical Museum, and point out some of the many interesting items of the Museum. (Here you can click and take a video tour through the castle.)
Then on to the Fredensborg Castle which is the Royal Residence for more than 7 months of the year. It is a very old tradition, that during the month of July it is possible to go on a guided tour through the private rooms of the castle and you can visit the private garden. Many tourists want to do that - getting to see how the Royal family lives is for most people more interesting than seeing just another museum-
castle. If the visit is not made during the month of July you might still want to take a stroll in the baroque park.
From Fredensborg we use the nice, narrow country road round the Esrom Lake to Tikoeb and via Gurre to Helsingoer (= Elsinore) with the Kronborg Castle(**).  Walking up to the Castle is a must if the weather is nice. There is a very nice view across the Oeresund to Sweden. But  the rooms of the Castle are very sparsely furnished - and really not that interesting. The Danish Maritime Museum is located in a part of the castle. That museum is interesting - it illustrates not only the history of the Danish merchant navy, but also Denmark's rather non - glorious role as a colonial power in India, Africa and  the Virgin Islands - but there is really no time to see that Museum on an ordinary  North Zealand tour.
After Kronborg we then drive back to Copenhagen using the coastal road, passing on the way the Louisiana Museum of Modern Art   (**) (probably the best museum of modern art in Denmark) and, in Rungsted, we pass the museum for the writer Karen Blixen (Pen name: Isak Dinesen), famous outside Denmark as the author of "Seven Gothic Tales" and "Out of Africa." 
We also pass The Deer Park with the small Eremitage Castle,
Taarbaek and Klampenborg with the Bellevue Beach, the main beach of Copenhagen.

In 5 hours it is possible to see Lyngby - The Open Land Museum - Frederiksborg Castle - take a walk in the garden at Fredensborg and taking a walk at Kronborg - but no lunch.
In 7 hours it is possible to stop for lunch and spend a little more time at some of the sights - or skip the lunch, grab a burger or a sandwich  and spend more time at the sights.