To blush or turn red in the face.
It's not an especially old phrase and isn't seen in print until 1836, in Frederick Marryat's Japhet in Search of a Father:
"Her ladyship coloured up with rage."
The verb colour was used earlier, as in this example from Samuel Johnson's Dictionary of the English Language, 1755:
"To colour, to blush. A low word, only used in conversation."