Kyoto Capital 1100th
Anniversary Medal
平安遷都千百年記念祭
Heian Shrine 1100th Anniversary Medal. Dated Meiji 28 [1895].

This is the larger version, most likely given for larger donations to the
shrine. The medal diameter is about 2.5 cm.
Heian Shrine 1000th Anniversary Medal. Dated Meiji 28 [1895].

Original case of issue.
In 1895, many festivities were held celebrating the 1100th anniversary of the capital of
Japan being in Kyoto, and to commemorate this anniversary, the
Heian Shrine was
established.

Such a large undertaking needed a lot of money, so donations were aggressively sought.
Large donors would receive a medal, and I am assuming the type of medal awarded
depended on the amount of the donation. Below you can see an award document, which
was given for a donation of 1 yen (obviously more valuable than today's yen). This
document could have accompanied a medal, or it could have been given in lieu of  a
medal since the amount wasn't high enough to warrant a medal. I'm not really sure...

These medals are all dated the same and most have the same inscription. But, as you
can see below, there are variations in cases, ribbons, attachments, and some of the
medal designs as well as inscriptions
Construction of the shrine (1894 photo)