While solemnization of marriage is primarily provincial jurisdiction in Canada, there are several relevant offences under the Criminal Code. Notably, sections 290-295 criminalizes bigamy, polygamy, pretending to solemnize marriage, feigned and forced marriages and any marriage contrary to law.
Section 293, which criminalizes polygamy, was the subject of a Supreme Court of British Columbia reference case in 2011. The court ultimately decided the law was constitutional.
Pretending to solemnize a marriage
Section 294 says:
Every one who
a. solemnizes or pretends to solemnize a marriage without lawful authority, the proof of which lies on him, or
b. procures a person to solemnize a marriage knowing that he is not lawfully authorized to solemnize the marriage,
is guilty of an indictable offence and liable to imprisonment for a term not exceeding two years.
While rare, there have been a few recent convictions under this section.
Dale Reade (also known as Dale Brewster), a Dorchester, ON woman, plead guilty to six counts in August 2014 after she performed a number of marriages without a license. While the maximum punishment is a two-year prison sentence, Brewster received 30 hours of community service and was required to payback the fees she'd collected for performing the ceremonies. Reports in the London Free Press at the time noted that prosecution and defence attorneys had difficulty finding any case law to guide sentencing.
One of the couples married by Brewster applied to the Ontario family court for an annulment. The case was dismissed, as section 31 of the Marriage Act of Ontario says that any marriage "solemnized in good faith...shall be deemed a valid marriage" even if the person who solemnized it was not authorized to.
In 2015, a Buckhorn, ON man was charged after a couple reported him to the police.
In December 2016, Michelle Buttineau of Parry Sound, ON was charged with two counts of pretending to solemnize a marriage following fraudulent marriages in February and June.
Aside from these local stories, there don't seem to be any cases outside of Ontario.
These cases highlight that Humanists and other people lacking government authorization cannot simply begin providing ceremonies in Canada.
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References:
More on the case of Dale Brewster. Jan 2014, August 2014, October 2014.