Among the royals who regularly wrote to Clementine, there were Queen Maria II of Portugal, Queen Marie Amelie of Portugal, Queen Marie Henriette of Belgium, Crown Princess Stephanie of Austria, Princess Louise of Belgium, Alexandrine of Baden (Duchess of Saxe-Coburg-Gotha), Ferdinand I of Bulgaria, his first wife Marie Louise of Bourbon-Parma, Princess Helena of the United Kingdom, etc.
There is a huge amount of letters from Queen Victoria to Clementine preserved in this archive. It seems that they were good friends since they wrote to each other during half a century.
Well, I am not surprised as they all belonged to one family. Everyone of the mentioned above was a member of Saxe-Coburg-Gotha dynasty, either by birth or by marriage. It doesn't matter that reigned in several countries, they were still family and it's natural that they corresponded since they all knew each other very well.
It would be interesting maybe to read published correspondence in some near future.