I can attest to the compatibility of Martin Logan and Carver, but you definitely want to use a Carver amp with a lot of "umph", because like someone else said here, those ESLs can present some pretty difficult impedence loads. (the Sequels, I know, can go all the way down to a 2-ohm load, depending on volume and the kind of music)
I used to drive my Sequels with a pair of Carver Silver 7ts, and they sounded fantastic. I'd tried Rotel, Tandberg, Sony ES, Quad, and listened to Krells, Mark Levinson, and Audio Research amps driving the Sequels, and to my ear, the S7t was the sweetest sounding amp with this speaker for under $10,000. I hear the sequels driven by a pair of Mark Levinson ML-3s once--that was nice. And they sounded particularly nice driven by a pair of Audio Research 100watt tube monoblocks, but those things were something like $10,000/pair a pair, and required dedicated 60 amp breakers on my power mains...
I still have my Sequels, and am planning to get a ML Cinema or Stage center speaker for my new home-theater setup (maybe even splurge and get a pair of Scripts for the rears...) and I'll more than likely drive them all with Carver amps (Unfortunately I had to sell most of my other gear a few years ago, du to being unemployed for a long stint).
So yes, I'll completely vouch for the sweetness of the ML/Carver combo, even if the folks at Stereophile magazine think it's not good (frankly I think that particular magazine just has it out for Bob...).
Hope this is helpful!