The small porringers are sometimes called posnets, which is an old-time word that may originally have referred to a posset-cup.
"Home Life in Colonial Days" by Alice Morse Earle
Will it be tea or a cup of ale posset?
"The Old Countess; or, The Two Proposals" by Ann S. Stephens
He was astonished when his spoon scraped on the bottom of that silver posset-cup.
"Norston's Rest" by Ann S. Stephens
She took the posset from the trivet, and, lifting the lid of the cup, looked in.
"The Man in Black" by Stanley J. Weyman