Talk directly to the cruise line's customer service or concierge service. For example, Princess Cruises and Holland America have arrangements with air carriers that bring the air prices down when booked through the cruise company. Ask the cruise agent what the airfare would be for the southbound cruise. Remember, you need to fly to Anchorage and out from either Vancouver, BC, San Francisco, Seattle or in rare occasions, Los Angeles.
Take advantage of ticket discounters and consolidators such as Priceline, Orbitz and Cheaptickets. Use the "one way" options as you need a one way ticket to Anchorage from your home city and another one way ticket from the cruise arrival city. Many times these online resources are able to locate deeply discounted fares. The downside is that these fares or typically non-refundable and may not be changed to different dates should something change on your cruise itinerary.
When it comes to getting cheaper airfare, timing truly is everything. Use two different "timing techniques" to gain cheaper fares. The peak Alaska Cruise season is between mid June through late August. Airfares, hotels, rental cars and cruise prices are at their highest during this time of year. If you have flexibility in your schedule, book your fare for late August or early September. This gives you a cheaper cruise and allows you to get the "shoulder season" airfare deals.
In addition, book your airfare as early and as far in advance as possible. As a general rule, air tickets purchases 21 days in advance are among the cheapest found.
Even if you don't have enough miles on a frequent flier program to qualify you and your partner for free tickets, most frequent flier plans have a form of discounting fares in exchange for miles. For example, Delta's Sky Miles program let's you use portions of your miles for reduced airfares. Because the airlines change the fare programs often, check with your preferred carrier's program for any current deals for mile exchange and fare reductions.