About three years ago our local games reinstituted the kirkin o' the tartans on Sunday morning. Its one of my favorite parts of the games!
When I was without a kilt (heaven forbid! ) my daughter & I would attend as our ancestors of old, holding a swatch of our clan tartan in our hand.
There are a lot of myths associated with the Kirkin' service:

http://scottishtartans.org/kirkin.htm

Regards,

Todd