I like to listen to pieces that were actually composed and performed for specific occasions in late Imperial Russian history. So far, I've collected the following on CD :
Coronation Cantata, by Alexander Glazunov (Op.56), first performed May 1896 as part of the celebrations for Nicholas II's accession, but somewhat overshadowed by events at Khodynka and hardly ever performed since. Available on the Chandos label and very fine!
The King of the Jews (Tsar Iudeyskiy), another cantata by Glazunov (Op.95), this time with libretto by none other than Grand Duke Konstantin Konstantinovich ('KR'), a gifted poet, pianist and composer. The whole piece (nearly an hour) was first performed by a large orchestra, choir and soloists in the Hermitage Theatre in January 1914, with KR himself taking the part of Joseph of Arimathea. Also available on Chandos.
Coronation Cantata, by Jean Sibelius, first performed in Helsinki 2nd November 1896 in honour of Nicholas II, the former Chancellor of Helsinki University and Grand Duke of Finland. Hardly (if ever) performed since. Sibelius was commissioned to compose the piece, which he did, probably against his will. There are political 'overtones' in the 30 minute piece, reflecting feelings of protest regarding Russian attitudes towards Finland. And there is an amusing story that the premiere of the piece was ruined by a drunken tuba player in the orchestra, who kept coming in at the wrong time and making disrespectful rasping sounds with his instrument!! It's probably only a story, as there is no tuba part in the score! Available on the Ondine label.
I could add Tchaikovsky's 'Moscow', which was performed at the coronation of Alexander III, and of course we know that Nicholas II was present at the premiere of the same composer's 'Sleeping Beauty'. At the end the Tsar said he thought it was 'quite nice' which offended Tchaikovsky very much!
Coming right up to date, there is a piece by John Tavener called 'Elizabeth Full of Grace' which celebrates jointly the canonisation of GD Elizabeth Feodorovna and the long life of Queen Elizabeth, mother of Elizabeth II. Available on Sony.
They're all worth listening to! I'm sure other people can add more to the list.