Both were deported to the Sardinian salt mines, and died after harsh treatment there. Pope St Pontian resigned in 235 in order to allow a successor to be elected in his stead.
The legend for St Hipppolytus however is more colourful, as the martyrology relates:
"At Rome, blessed Hippolytus, martyr, who gloriously confessed the faith, under the emperor Valerian. After enduring other torments, he was tied by the feet to the necks of wild horses, and being cruelly dragged through briars and brambles, and having all his body lacerated, he yielded up his spirit. On the same day, suffered also blessed Concordia, his nurse, who being scourged in his presence with leaded whips, went to our Lord; and nineteen others of his house, who were beheaded beyond the Tiburtine gate, and buried with him in the Veran field."