Fog in the San Juans comes in two forms: everywhere and unavoidable (and obvious), and highly localized. For everywhere fog, you just wait it out and check the dew points as noted. Usually it clears by noon (or earlier) but occasionally lasts almost all day.
As for localized fog, it can be a surprise. It may be clear in Friday Harbor, for example, but have thick fog between Shaw and Lopez (that's a common pattern) or clear at Anacortes and foggy in Rosario Strait, or clear at Rosario Resort and foggy in Thatcher Pass. As noted clear skies and relatively high dew point are indicators. One surprise is that it often starts out clear in the SJs and then fogs up an hour or two after sunrise!
A good tool in those cases is the radio + AIS -- find other vessels on AIS and ask them what's going on where they are (using channels 68, 69, 72 after hailing on 16). I have navigated heavy fog from FHR to Cattle Pass on the basis of radio assurance that it would be clear in the Strait of Juan de Fuca (and it was, clearing up right at Cattle Pass. Would not have wanted to cross the Strait otherwise.)
Adding to the others here, I also check general aviation airport reports (an app like Avia Weather, using near-water airports like KFHR, KORS, KBFI, etc.) and also the Webcam feature on Windy (ferry terminal cameras can be very helpful).
Currently looking out my window in Seattle I see clear skies and the Olympic Mountains. But Boeing Field just a few miles away reports low instrument conditions with 400ft ceiling! SeaTac reports 100ft ceiling. So I know there must be some fog out there. If I were headed out, I would check webcams around my destination, and AIS tracks for more insight.