Two friends (baptized Protestants previously married to other Protestants) are marrying each other. They have applied for annulments of the earlier marriages. If annulment petitions are granted, do they need to have their marriage blessed in the Church?

No. As soon as both annulment petitions are formally granted, your friends’ marriage to each other will automatically be recognized by the Church.

Here’s why: At the time your friends married each other, the only canonical obstacle to their wedding was ligamen, the fact of their prior marriage bonds (Canon 1085). But if annulments are declared for both prior marriages, that means that at the time of their marriage to each other your friends were canonically free to contract marriage and the manner in which they chose to marry would have been lawful for them at the time. Thus, their second marriage could be recognized without any further qualifications.