The most famous monarch held for a King's Ransom was of course Richard I (the Lionheart), held to ransom 1192-1194 held by Henry of the Holy Roman Empire. His mother Eleanor of Aquitaine worked to raise the 150,000 marks demanded (around 100,000 pounds, maybe two to five times the annual Crown income at the time, depending on which account you read), by heavy taxes on the church and people. These taxes could be up to a quarter value of property owned, but it was worth it to get rid of nasty King John.
Bertrand du Guesclin, brilliant 14th century French soldier during the Hundred Years War, was captured by the English at Auray in 1364. Charles V of France paid his ransom, but he was captured again whilst commanding French mercenaries against Peter the Cruel of Castille (who had enlisted the help of Edward the Black Prince of England). Du Guesclin had the last laugh against the English as in subsequent campaigns he re-captured sizeable chunks of French territory for the home side. He died on a campaign in the south in 1380.
A little later on, James I of Scotland, held to ransom 1406-1424 by Henrys IV and V of England, was treated as a royal guest. James married the Earl of Somerset's daughter before his return to Scotland, where he reigned until 1437; although he pushed through many good reforms in Scotland , he made enemies and unfortunately James was assassinated aged 43.