Elisa was the fifth of eight children of prince Anton Radziwill and Luise of Prussia . She received a very good upbringing and was very musically and artistically talented. Because Elisa often visited her mother's home, she and William had known each other since they were very small children. The first hints of romance came when the two danced together at a ball in 1815. At the time William was 18 and Elisa 12--shades of Fritz & Vicky and later on Nicholas & Alexandra. On 27 January 1821 they performed together in a family tableaux and Elisa, which had the title part, aroused general admiration--being described as the most beautiful lady of the Prussian Court, calling her an "angel" and the "white rose".
The drama of their romance played out over the course of several years--from roughly 1820 to 1826. Wilhelm stood after his brother Friedrich William in the succession to the throne and was required to make a suitable marriage. Elisa's parents and Friedrich William III tried to prove the equality of the Radziwills to other royal houses but it was insufficient.
When this avenue failed, Friedrich William III, in 1824, turned to Alexander I of Russia (William's sister Charlotte was Alexander's sister-in-law) with the request to adopt Elisa. This the Tsar rejected however. The second adoption plan by Elisa's uncle, August of Prussia, failed likewise, because the responsible commission found that adoption does not change "the blood" . There were also several political and royal factions allied against the marriage. Heavy pressure was brought to bear on William to give up the idea of marrying Elisa. Finally the king was forced to recognize the impossibility of the match and in 1826 demanded from Wilhelm the renouncement of the idea. William obeyed. The two would occasionally still encounter each other, however. Elisa became engaged to Friedrich of Schwarzenberg but it was later broken off. William last saw Elisa in 1829. In 1831, Elisa was diagnosed with tuberculosis and spent most of her remaining years in more suitable climates. She died in 1834 and her coffin was moved in 1838 to a newly-built family mausoleum to lie next to her father. Wilhelm never forgot her though, and much like his grandson and namesake William II, kept a portrait of his lost love on his desk the remainder of his life.
Their history was made in to a movie in 1938 with Lida Baarova in the role of Elisa. With the outbreak of WWII in 1939 the film was forbidden, since a relationship between a Prussian prince and a Polish princess did not appeal to the Nazi regime.
You'd think this doomed romance might have made William more sympathetic to his granddaughter Moretta's wish to marry 'down' with Alexander Battenberg. Perhaps it worked in the opposite direction though--having renounced his own true love for duty and politics, he expected no less from his granddaughter.