The briefing recommended either the GBU-24s or the Walleyes. Also in my experience the naval SA-11s do a pretty good job of shooting down Harpoons, even if you set them to low-altitude skimming flight.
I thought that issue was fixed in TSH 4.02.
Originally, there was an error in the RCS setting for the Harpoon. It basically had the radar signature of an F/A-18 and was very prone to getting shot down by SAMs. A workaround was to use a SLAM against Naval Targets since the RCS was correctly set as much smaller, and had greater probability (though not 100%) of penetrating the anti-missile defenses.
My tactic (often resulting in untimely ejection, I have to say

) was to fire the Harpoon/SLAM at max range, then burner in at low level so I pretty much overtook the missile and had an envelope to launch HARM. Since the HARM travels faster than the Harpoon/SLAM and was fired somewhat ahead of it, there was a good chance to take out the radars directing counter-fire at the shipkillers before they could engage them.
Holding wingies out of range and ordering them to fire only after HARMS could do their job also allowed their Harpoons to get through. I don't know that I actually succeeded in the campaign mission with this tactic, but it worked against smaller naval groups in custom scenarios. Even better in Multiplayer where you could have a section of devoted HARM shooters with the AGM-84's carriers hanging back.