Nice ones :)
It's the participation medal for the 2. Danish-Prussian war (1864). This - and the participation medal for the 1. Danish-Prussian war (1848-50) - are the most common Danish medals. Around 46.000 1848-50 medals awarded for the 1848-50 war and around 58.000 1864 medals awarded for the 1864 war (and 3.000 1848-50-64 medals awarded to those who participated in both wars).
They were not awarded until 1876(!) because of the usual political mess, so many of the participants - at least those who fought in the 1848-50 war - were already dead.
It looks like new ribbons - original ones are usually quite dirty...
It was meant to hang from a straight ribbon, but as the official Danish ribbon style changed to the 'pentagular' one around 1900-1920, many 'modified' the suspension to accomodate the new style.
/Mike