Several database sites, including ones at the Provincial Archives of New Brunswick have a "contains" option. This is particularly effective when searching for "Neil" which may be rendered as Neil, Neill, ONeil, ONeill, McNeill, etc. A search for "contains" Neil will catch all those variant spellings. Look and see if the site you are using supports this option.
The marriage bonds for New Brunswick are here for those who'd like to play with this option http://archives.gnb.ca/APPS/GovRecs/RS551A/?culture=en-CA