We have just done both our hives 2 weeks ago with GM queens, took the old queens out at the same time as putting the new ones in.
We used a push cage 100 x 150mm, made sure that they had some emerging brood in the cage with them, and some stores. one didn't have enough stores, so we added some fondant.
We left them in the cages for 4 days, then let them out once they looked happy with the new queens. both were greeted with antennae touching and licking.
The weaker hive accepted the new queen really quickly and was fatter and laying after a few days more. the stronger hive didn't show any signs of eggs or larvae on the next inspection and had drawn 7 emergency QC's.
We spoke to the supplier and he explained that with a good strong colony there is a possibility of "mild rejection" they just ignore her and its 50/50 if the will kill her or not, we inspected today, with a nuc to hand, just in case things were still bad, but she is much fatter and lots of eggs & larvae and no charged QC's so it looks like they have decided her pheromone is good enough.
Think this is why the suppliers recommend to introduce a new queen into a small nuc.
From this steep learning curve, would not introduce a new queen to a full summer colony again, and both hives were good natured and productive, the only reason we were changing was they swarmed at the first chance.