My usual MO before shield tech was to direct my missile strikes at the AMM bases before anything else, and after I started fielding shielded ships, I would bring at least one ship that could fully absorb at least one AMM salvo, because if you order the ship to reverse course as soon as the salvo is launched (and even meager thermal sensors can detect an AMM at its max range), one is all you're going to get, and if you can absorb one, you can absorb them all. However, while dealing with AMMs in that manner, I've discovered a rather exploity way of negating them almost entirely: because the AI does its interception math incorrectly, presumably due to rounding issues, if your ship ends its turn at just the edge of the AMM's launch range and immediatelly starts backing away, the AMMs will often, but not always, run out of fuel and miss on the same increment they were going to strike the ship. The launch range depends on the AMM's speed, range and the speed of your ships, for example my Precursors' AMMs have 60 kkm/s speed and just under 2 mkm range, and their launch range is ~1.6 mkm against my 10 kkm/s older generation ships and ~1.3 mkm against my fighters.Off-Topic: AMM evasion with fighters show
I'll admit that despite a non-insignificant chance of failure, this is still a very busted tactic, especially if you wouldn't be able to defeat the enemy AMMs otherwise, but in case your shields are already powerful enough, it just saves you so much time and so many clicks.
I rarely have these issues, it is all about overwhelming force. Simply go into your own AMM range and saturate their defences with your own AMM and ASM missiles at the same time, move in and blow them up.
Make sure you have overwhelming force at all times. If you don't then don't engage.
This will work pretty much all the time. This also is why gathering intel of enemy capability is key in all situation so you know if you should engage or withdraw.
That's great until you run into something you can't just roll over like a landslide :P I mean what if the hostile decides they want to invade Earth? It DOES happen!