The following is one of many lines tracing Elizabeth Willoughby to Charlemagne. This line goes through 11 males and 13 females. There are over 100 other ways to trace Elizabeth back to Charlemagne (!); I tried to pick one of the more interesting lines, which included a smattering of individuals from several of the Royal houses of Europe: England, France, Aragon, Hungary, Lorraine, Italy, Flanders.
1. Elizabeth Willoughby 1512-1562 = Sir Fulke Grevill, knight
2. Edward Willoughby = Margaret Nevill b. 1494/5
3. Richard Nevill, Lord Latimer ca. 1458-1530 = Anne Stafford
4. Sir Henry Nevill d. 1469 = Joan Bourchier
5. George Nevill, Lord Latimer ca. 1414-1469 = Elizabeth Beauchamp
6. Ralph Nevill, Earl of Westmorland = Joan Beaufort ca. 1379-1440
7. John of Gaunt, Duke of Lancaster 1340-1498/9 = Katherine Roet
8. Edward III, King of England = Philippa of Hainaut 1311-1369
9. William III, Count of Hainaut = Jeanne de Valois d. ca. 1352
10. Charles, Duke of Valois 1270-1325 = Margaret of Naples
11. Philip III, King of France = Isabella of Aragon
12. Jaime I, King of Aragon = Yolande of Hungary
13. Andrew II, King of Hungary = Yolande de Courteney d. 1233
14. Philip de Courteney = Yolande of Flanders 1175-1219
15. Baldwin V, Count of Hainaut = Marguerite of Lorraine 1140/5-1194
16. Thierry of Lorraine, Count of Flanders d. 1168 = Sibyl of Angou
17. Thierry II, Duke of Lorraine = Gertrude of Flanders ca. 1070-1117
18. Robert le Frison, Count of Flanders ca. 1035-1093 = Gertrude of Saxony
19. Baldwin IV, Count of Flanders 980-1036 = Otgiva of Luxembourg
20. Arnold II, Count of Flanders = Rosala of Italy ca. 952-1003
21. Berengarius, King of Italy d. 966 = Willa of Arles
22. Adelbert, Margrave of Ivrea = Gisele of Italy d. 910
23. Berengarius I, King of Italy 850-924 = Bertila of Spoleto
25. Eberhard, Margrave of Friuli = Gisele 820-874
26. Louis I, Holy Roman Emperor 778-840 = Judith of Bavaria
27. Charlemagne, Holy Roman Emperor 747-813/4 = Hildegard of Swabia