In early June you will see highs in the upper 50's and low 60's. Lows will be in the 40's. There is always a chance of rain on the Inside Passage.
However: You may see temps in the 70's.
The best thing is to dress in layers. A shirt, sweatshirt and water resistant/proof jacket are the best things to wear. Jeans or other types of rugged pants are also a good choice. Tennis shoes are fine for regular excursions. If you are going to hike then more rugged footwear is required.
A cheap poncho or rain suit is also a must.
Take care and enjoy the beauty of Alaska,
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Alaska cruises tend to be more casual than others and I found this to be true. Daytime wear and non-formal nights were very relaxed -- even jeans in MDR. But Formal nights were very dressy. It just seemed like people brought less dressy clothes with them and more functional clothes.
RCCL Serenade of the Seas
The part about dress in the MDR depends on the cruise line.
Some enforce the no jeans , etc in the NDR at night . Others don't .
If we knew the cruise line probably could give a better answer.
The weather during the day is very changeable , rain , sun , clouds
and snow within a space of an hour . Especially on tours that take
you to higher elevations or on the glacier.
Be prepared for all types of weather. Some years the temperature
in the Seattle/Vancouver area could 80+ degrees.
Go to the following link and search for the historical weather with the
For sure the layered clothing for Alaska and most important is rain gear, chances are, you will see it at some point. Have you decided on any excursions? There are so many good ones, its very difficult to pin point the ones you really want to do, so have fun planning that out.