Here are some poems released, as is traditional, by Their Majesties the Emperor and Empress of Japan at the end of last year (oh, all right, here's the English version), and here are a whole bunch of poems read by various members of the imperial household at this year's New Year's Poetry Reading (歌会始). Unfortunately the English version only includes a few of them, and to be honest I'm not sure it would be wise to barge in and take a crack at it myself.

I didn't know there was a whole separate word for "poem composed by the Emperor", but there is. It's 御製, gyosei, and it's made of the prefix that usually gets translated as "honorable" plus the word for "make".