Is there a cost for donning or doffing a shield and armor during combat?

Shields: as weapons. 13th Age did away with the buckler/light/heavy/tower distinction, so all you get out of shields is basically a +1 AC for a free hand if your class is proficient. No reason why rotating your weaponry as a quick action wouldn't also set up your shield.

Armor: not really a combat thing. If you get suckered into a combat without proper armor on, you're probably stuck there? Though the GM's got free reign (per p.164, "Dicey Moves") to decide if an attribute check might be an appropriate thing to do during combat to accomplish a task. If you got into a fight without your armor but it was right there, or you needed to get it off for some reason, your GM could make a call for action, upside, and downside, but we've left the realm of the rules far behind at that point.