score:4
Quite easy to recall the siege of Tunis, 1270 by Louis IX during 8th Crusade.
Also 5th siege of Gibraltar in 1349-1350, where Alfonso XI died of that very same "black death".
In both cases the besiegers heavily suffered of epidemies and had no success.
Upvote:2
In fall 546, Gao Huan launched another major attack on Western Wei, apparently to make one final attempt to destroy it. He put Yubi under siege, intending to attract Western Wei forces to Yubi in order to destroy it, but Western Wei did not respond. The general in charge of defending Yubi, Wei Xiaokuan, however, defended against all kinds of siege tactics that Gao Huan tried, for 50 days, and Eastern Wei forces suffered 70,000 deaths from the battle and the illnesses. Gao Huan himself was physically and emotionally drained, and he became ill, and he was forced to withdraw. Western Wei subsequently declared that Wei had killed Gao Huan with a powerful crossbow, and Gao Huan, in order to dispel the rumor, appeared before his army to sing Chile songs with HulΓΌ Jin. As he did, he wept bitterly.
https://en.wikipedia.org/wiki/Gao_Huan#During_Emperor_Xiaowu.27s_reign
Most causalities in this battle was due to plague.
Upvote:3
The most obvious example would be the Siege of Kaffa, in which the Golden Horde tried to take control of what was then a Genoese colony, situated on Crimea. However, the Black Death spread in the mongol army, and they had to abandon the siege. Before they left, they hurled dead corpses into the city, in the hope that the plague would spread. It eventually did, and from there to the rest of Europe. Here is a blog post discussing the more medical aspects, which also cites a primary source in some length.