British Columbia and the North West Territories border the Pacific Ocean, but the NW Territories are not a province.

There are two provinces and territories that are in the Western Cordillera. British Columbia and Yukon are the two that border the Western Cordillera.

The Yukon Territories, and British Columbia border the Pacific Ocean.

British Columbia

As far as provinces go, British Columbia (particulary the northern part of it) would fit the bill. The Yukon and Northwest Territories are in Canada's western and northern land, although they are territories and not provinces.