CAR 257 (6) (b) states that you can only continue to a destination when conditions are below weather minimums if you are certain you will be able to gain visual reference to land on arrival.
(6) This regulation does not prevent a pilot from:
(a) making an approach for the purpose of landing at an aerodrome;
or
(b) continuing to fly towards an aerodrome of intended landing
specified in the flight plan;
if the pilot believes, on reasonable grounds, that the meteorological minima determined for that aerodrome will be at, or above, the meteorological minima determined for the aerodrome at the time of arrival at that aerodrome.
I would say that if METARs(SPECI) were indicating that conditions were worsening below alternate minima and trending towards landing minima you would be losing your "reasonable grounds" if you then arrived and conditions were below landing minima. This is unless there was an inter or tempo or some other transient effect which could explain the conditions and you had fuel available to hold.
ENR 58 is mainly for planning purposes but also would most likely cover you for the reasonable check en-route as well.