When I was a child growing up in Dublin the blessing of throats on the feast of St Blaise took place only in the Franciscan and Capuchin churches, as I recall. Apart from my memory, the only evidence I have been able to find of this is from a bulletin of the Augustinian church in Limerick, Ireland, a year ago: For many centuries devotion to St. Blaise, a fourth century Armenian bishop, had almost completely disappeared. It was kept alive in some Franciscan churches. On the 4th February 2004 the Limerick Chronicle published a picture in its memory section, a clear photograph of a long queue in the local Franciscan church lining up for the blessing of the throats on the Feast of St Blaise. The Friars stood in the sanctuary for the entire day ministering the healing of this popular saint to those who streamed in and out of their church on Henry St.
I have a vague recollection of red flannel, a sort of rough cloth, and of oil being associated with the blessing. The Wikipedia entry on the blessing of throats mentions oil.
Now the blessing of throats is widespread again with the priest holding two unlit candles to the throat of each person while praying this formula: Through the intercession of St Blaise, bishop and martyr, may God deliver you from every disease of the throat and from every other illness: in the name of the Father and of the Son and of the Holy Spirit. Amen.
The Fourteen Holy Helpers [Wikipedia]
St Blaise is one of the Fourteen Holy Helpers, saints invoked against various illnesses. That's where the connection with Englebert Humperdinck - the German composer, not the English singer whose real name is Arnold George Dorsey - comes in. In his opera Hansel and Gretel contains this song, The Evening Prayer, when Hansel and Gretel are lost in the forest:
Fourteen angels watch do keep,
Two my head are guarding,
Two my feet are guiding;
Two upon my right hand,
Two upon my left hand.
Two who warmly cover
Two who o'er me hover,
Two to whom 'tis given
To guide my steps to heaven.
The 'fourteen angels' are the Fourteen Holy Helpers. Here it's sung by Libera, a boys' choir from England.
St Blaise was a bishop Sebaste in historical Armenia. The area of which he was bishop is now part of Turkey and under the jurisdiction of the Archeparchy of Istanbul (Armenian). The Armenian Catholic Church is, with fewer than 500,000 members, one of the smallest of about thirty churches that are fully part of the Catholic Church. The largest by far of these is the Roman or Latin Church but all are equally Catholic and in full communion with one another and with the Pope.