Hello, Auchencrieff - what a coincidence! I'm not connected to the Shileds but I am in the process of helping a friend in that research! I live in Bathgate.
Margaret Boyle died, as you know, in Russell's Row, Bathgate, on 6Nov1864. She was the widow of Terence Shields, a coal miner. Her death was reported was reported by her son, Peter, who married Catherine Brogan in 1863 in Bathgate.
Margaret was interred - interment no. 733 - in common ground in the Bathgate Paulville Cemetery - Lair no. N37 - on 8Nov1864. She was aged 67 years and described in the Burial Register as "wife of the late Tery Shields, miner, Airdrie".
The person I'm helping is also Peter Shields who is descended from John, Peter Shields and Catherine Brogan's first son - born in Bathgate in 1864.
I see you're in Canada - do you know Cathie Grant?
Tom