You may not have thought about it, but the SCA itself is period. At the least, the idea of recreating the combat and chivalric stories of olden days was practiced starting as early as the 13th century and going well into the 16th (and 20th). So in that regard, not only can a tournament form itself be period, but it is also period to actually plan and hold a creatively anachronistic tournament.

From a surprisingly early time, some tournaments were based on, or styled after, the Romances, stories of knights and adventure. In 1240 a knight named Ulrich von Liechtenstein undertook a quest. Ulrich dressed as King Arthur and was accompanied by six friends who took on the names and traditional costumes of six knights of the Round Table. They traveled through Austria in search of jousts and melees. Amoung those who answered their challenge was Frederick, Duke of Austria. Knights who did well against this company of Arthur's were rewarded with admission to the Round Table.

Even earlier than that, in 1227, Ulrich had disguised himself as Venus (don't ask) and undertaken a month long quest to honor the lady whose love he sought. Traveling from Venice to Vienna, he wrote that he broke over three hundred lances and awarded nearly as many rings. He also claimed that his disguise was never seen though. A bit of silliness with one's combat, it seems, is also period.

In 1278, a tourny was held in Picardy (France) which not only used the tales of Arthur and his knights as its theme, but which also involved some story line and scripting. The combatants arrayed themselves in Arthurian dress, one lady acted as Queen Guinevere and another as Dame Courtoise. At the start, some of the knights surrendered themselves to the Queen, claiming to have been defeated by the 'Knight with the Lion', who arrived in triumph shortly there after. The combat revolved around the plight of one Lady, who was to be punished by her lover for declaring that Arthur's knights excelled all others in feats of arms and courtesy. It was the job of various knights present to prove her claim true so that she would not be harmed.

Some tournies clearly involved some measure of research and anachronism. Maurice Keen discusses a late 15th century 'Quest' in which the combatants not only wore the heraldic devices of Arthur's knights, but also readied themselves in armor of an archaic style before setting out, damsel and attendant alongside them. This tourny, and others, may also have involved riding about the woods like a knight errant, fighting chance encounters with other tourny participants.

Other events pressed the line between tournament and theatre. A tourny sponsored by Mary of Hungary in 1549 involved at quest to free prisoners held by an evil enchanter. To free the prisoners, the combatants needed to reach 'Fortunate Isle' and draw a sword from a stone pillar. In order to gain the isle, it was necessary to meet in combat three knights. Those who were defeated joined the prisoners. Those who succeeded in reaching the sword discovered that only a Prince could remove it from the pillar. Phillip II, heir to the emperor Charles V, won the tournament. But we already knew that rank has always had its privileges.

Some books that deal with tournaments are:

Chivalry, Maurice Keen, Yale University Press, 1984

A wonderful book. It doesn't have a lot of pictures, but its text is through and readable. Chapter titles include The Rise of the Tournament, and Pageantry, Tournies and Solemn Vows.

Knights, Andrea Hopkins, Grange Books Plc., 1990

This book has some particularly nice passages on tournaments and includes some detailed descriptions of a few historical quests and challenges. Also some very nice illuminations.