Elements of Coronation
Anointing involves having some part of the king's body being touched by a finger or piece of cloth which has been dipped in holy oil. It was originally a Hebrew practice. It was adopted by Pippin the Short as a symbol of the papal, and therefore divine, blessing of his reign.
Raising upon a shield
Being raised on a shield is a symbol originated with tribal chiefs. It symbolises that the leader is a first among equals, and whose rule is dependant on those who support him. It was used by the Franks in the coronation of Clovis, and may also have been used as late as that of Pippin the Short.
Coronations in the SCA
Most coronations involve the previous rulers stepping down and the new rulers taking the throne, followed by oaths of fealty from peers and populace. A public reading of new laws and goals for the reign then occurs, and the coronation ends with a procession. Kingdom business tends to wait until the first court after coronation (some wags in Ealdormere refer to the first court as "taking the shine off the hat").