If you try to install .NET Framework 4.5.1 on a fresh installation of Windows 2008 R2 Server Core you may see the follow error message:

You must install the .NET Framework 2.0 SP2 OS component.

Well, there IS a link to a list off reasons for a blockage of the 4.5.1 installation, but it wouldn’t be Microsoft if that error message is really in the list. After having a look at the listing of available features, I tried NetFx2-ServerCore first, which should be sufficient on a 64bit platform. Error message still occurred, so I installed the 32bit compatibility feature NetFx2-ServerCore-WOW64 as well. There we go: .NET Framework 4.5.1 could be installed successfully.

As searching for the error message did not return any useful results, I am documenting the solution here.
For completeness, here are the two commands that install the missing features on Server Core:

dism /online /enable-feature /featurename:NetFx2-ServerCore
dism /online /enable-feature /featurename:NetFx2-ServerCore-WOW64