Catflier is correct that there is no direct support (at the API level) for MIDI in WinRT. However, if you are wanting to have MIDI-like capabilities in your app, there are workarounds. A protocol growing in popularity is the network-based OSC (Open Sound Control). Since it is network-based, you can use that.
For example, one can use external hardware like The Missing Link which translates from MIDI to OSC. You hook up your MIDI device to The Missing Link, which then translates to OSC messages that are sent to the computer. Your app can then receive OSC messages and talk to the MIDI device. I don't have any code to show here, but I've seen demos of this working in-action.
You can see OSC in use on iOS as well with popular apps like TouchOSC.