Well, depends on where in the 12th century... some Indian and East Asian fencing weapons were meant to be deployed as a pair. I am assuming you mean medeval Europe.
The earliest tome on swordsmanship is an untitled work known simply as I.33, and dates to 1300. It concerns itself only with buckler and longsword, which were in fashion at the time. Later into the 14th century, the aphorisms of Johannes Liechtenauer were recorded by contemporaries... but they made no mention of dual-weapon technique.
Any fighting technique used by feudal knights or soldiery earlier than this is not documented by history - accounts of battle generally notes who killed who, not blow-by-blow reconstructions of the melee. Likewise, art depicting battle usually modelled the knights in their finest regalia, not in the disarray of actual combat.
Considering a shield is a weapon in its own right, and one the medeval combatant had likely trained with, they'd go for an abandoned or improvised shield before a spare sword if they found their shield hand empty.