After some research, as extensive as possible solely online, and aided by thefind.com, I settled on these sets (click to go to the online store):
Both are magnetic, and are alleged to have strong magnets.
The first is a mere 7.5" board, but it doesn't fold (which I like), and it has a drawer (meaning that I can set up and tear down without pouring pieces all over the place or even move the board). The price: $29.99.
I went for size with the other: a folding board, since the price was much lower for a folding board of that size (12") than for a board with a drawer. This one costs $39.99.
They have a claimed retail price of $79.99 each, which seems a bit exaggerated to me after seeing other stores' prices for similar sets. I would place the value around $65 for the larger and $50 for the smaller based on other prices.
I considered buying their 12" drawer set ($79.00) in lieu of both the above, but decided against it, since it would end up costing more, and at this point I would rather have two sets.
Another set I was seriously considering is sold by another store.
I like this idea, since not only does it have a handy place for captured pieces to go, it also can be closed up in a certain position to be played later.
I'll update later on how the ones I purchased turn out.
Edit, a week later: I've just received the sets, and though one was not the exact set I ordered (hinged w/ board on top instead of a drawer), the sales rep I contacted is going to initiate an exchange shortly. The other set was better than my expectation, with smoothly finished wooden board and pieces, and inlaid wood squares. No magnets are visible, and the pieces fit snugly in the carved felt inside the box. It's a handsome size and convincing weight, and the pieces are the same. I believe I would have paid more for it.
My review of the other set will have to wait until it arrives...
Edit, two days later: I talked to the sales rep again, and he let me know that they actually do not have any drawer sets of that size, and that a item number mixup led to advertising of a 7.5" x 7.5" drawer set instead of a 7.5" x 7.5" hinged top set. He offered to pay return shipping as well as the refund, but also gave me the option of keeping the set and letting him send me a 5" x 5" drawer set free of charge or a $20 discount on a larger set. Naturally I appreciated this offer very much, and accepted the 5" x 5" set. So now I will end up with three sets. I unpacked the 7.5" set which I had set aside, and tested it.
The magnets are not as functional as the ones in the larger set, and three of the pieces had virtually no "stick" to the board and would readily slide off when tilted sideways. (They would stick pretty firmly to the refrigerator, though, so that was partially the board's fault). All the rest of the pieces wouldn't move if carefully rotated sideways and upside down, but almost any motion while sideways would cause some pieces to slide slightly. Other than that, it is another well-put-together set that seems as if it will last a lifetime.
Now naturally I couldn't live with the three nearly nonmagnetic pieces, so I peeled off the felt of one of the faulty pawns, pried out the magnet, and had a look. It was a cheap, grainy sort of magnet, but strong enough for its size that I almost gave up trying to come up with a better substitute. Suddenly I bethought myself of some old Magnetix kits we had stored away. Armed with pruning shears, I removed a magnet off the end of one of the toys. It was about the same diameter as the chess piece's magnet - a smidgen smaller, but twice as thick, and at least twice as strong. I drilled the pawn with a power drill to make room for the new magnet, fitted it tightly in, so it didn't need glue, and glued the felt back on with white glue. Voila! A pawn resurrected! I did the same with the other two pieces, but after I placed them on the board, I discovered that I would like all the pieces to be that strong. For the next two hours, I removed Magnetix magnets, peeled off felt pads, pried out magnets, drilled holes, forced in magnets, glued on pads, and set the pieces on their sides to dry overnight. The next morning, I was suddenly very fond of my chess set. The only drawback to the stronger magnets is that the pieces tend more now to stick to one another if you are not careful with a piece in transit near other pieces. It isn't on the level of a big problem, though, and I like the new magnets much better than the weaker ones. Now I can shake the set while it's sideways, and only the Black king will move (I must have set the magnet too far in).
Bottom line: I would recommend this set in its original form but with the warning that the pieces will not have very strong magnets. Strong enough to carefully turn it sideways/upside down, but not much more.
Later I will review the 5" x 5" drawer set.
Edit, nine days later: The 5" x 5" drawer set was much better in nearly every aspect than I expected. The magnets were strong enough to perform well even during such antics as I described for the other two sets. No slipping at any angle, even with moderate shaking. Yet they are not so strong they pose problems in sticking to one another. And, as with the others, the board and pieces are very smooth and pleasantly glossed.
The drawer slides with enough resistance that even when partially open, it cannot accidentally slide out. It can be slid all the way out on either side, free of the board if desired. It has a spring ball mechanism which fits into an internal groove for additional "hold" when the drawer is in its closed position.
I am very satisfied with these sets.