I bought two queens from Easybee.
They were in these bee cages, below.
I was confident about one of the hives. It had been queenless for some time (but see next post). So I knew it would accept a new queen.
The other hive I was worried about. Through pressure of time, I was not able to leave a day between killing the old queen (who was not laying) and introducing the new queen.
The result? Both queens laying very happily.