Have you ever been in a position where you needed a quick break but your players were too ancy to break as well?
When dealing with nobility and court settings, players can sometimes skip the roleplay aspect and jump straight to behavior such as, "I bow, greet all in the court, and ask the duke for his assistance." While in most scenarios this type of action is sufficient, taking it a step further can enhance gameplay (or maybe even manipulate a plotline).
Rather than making a baddy impossible to hit, consider giving it mega-hit points.
Super hard to hit leads to great player frustration. Allowing them to do damage leads to a sense of accomplishment. another variation of this would be to give the bad guy a forcefield that shows damage.You could also give them a mastermind ability that sluffs the damage of to minions who should be easy to kill.Once in a while a super high to hit encounter is ok ,but it should be few and far between.
Your mileage may vary