The most cursory possible search (ie. I went on Wikipedia) states that the last execution for heresy in the nineteenth-century. Was this the last heresy trial (successful or not) or did the practice continue into the twentieth-century?
Extra Credit: What were the theological or liturgical developments to combat (or explain) the proliferation of Christian heresies post-Reformation?
I restrict this to the heresies trials held by the unam, sanctam, catholicam et apostolicam Ecclesiam or bodies pertaining!
I can't be sure it was the most recent trial for heresy, but the Roman Catholic Church did try Fr. Ned Reidy for heresy in December 2005. He was found guilty by a tribunal in the Diocese of San Bernadino of heresy and schism. If you need further data, searches for "Reidy" and "Heresy trial" will bring up several news sites, and some official documentation. Strictly speaking this breaks the 20 year rule, but it certainly counts as a very recent heresy trial by the RCC.
I don't see how talking about the "unam, sanctam, catholicam et apostolicam Ecclesiam" restricts your question, since that is a confession common to many church traditions, not only Roman Catholicism, but that seems to be what you are asking about.