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I'm trying to georef old maps från 1960 that have clear boundary lines and my employer want an almost exact match with today's boundaries.

But it's very hard with 1th, 2th and 3th transformation. With adjust och spline it's possible. But my boss says it will change the image and it can't be used.

Do spline or adjust change the original image? How does they work?

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You could try and georeferenced online. http://www.davidrumsey.com/view/georeferencer

http://projects.iq.harvard.edu/cga/announcements/worldmap-map-warper-online-geo-referencing-tool

or if you have any software, you should be able to do it. I have a old St Petersburg, Russia map but still don't have the time to do that. I might give a try on one of those I mention.

You can google "georeferenced old maps online"

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You did not said anything about the software you are using. I will offer an explanation for ArcMap from the ESRI GIS suite.
Depending on the scale of the map, the boundary lines will be placed almost exact, or approximated. For an almost exact placing you will need a map with at least a scale of 1:5000. Use a current topographical layer from arcgis online and try to find common places that appear on the 1960 map and current topography; road intersections, buildings, waterways, railroads, etc.
Here is a how to interpret the transformations available for georeferencing. The higher the order of the transformation, the higher the number of points needed.
For more details, be more specific on your question after you use google and don't find anything relevant there.

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