Cents to Get Debt Free says it's no problem.
Actually we didn't have a microwave until a couple of years ago, when one was passed on to us from a relative. Our secret? The toaster oven--that's mostly how we warmed things up, baked on hot days, and so on.
Our problem? Toaster ovens, like so many other things, are not made nearly so well as they used to be. Twenty years ago I was using one that lasted for several years--we replaced it after we were married, mostly because it was looking pretty much the worse for wear. The one we bought then lasted several years.
And the ones we've had since then? Too many of them, and they all lasted approximately two months beyond the warranty period, never mind whether they were digital or basic-style, small or pizza-sized, bought at the Big Discount Place or at the Small Reputable Hardware Store. We just had another one bite the dust, and I'm missing it, even though it was one of the smallest ones we've had (didn't fit a casserole dish properly) and never did bake as well as the others. There are lots of times in the summer that you just can't turn the big oven on, and microwaving isn't always the answer.
But we don't want to buy another meant-to-fall-apart. Mr. Fixit even thought of looking for, say, say, a 1975 model on E-bay, but it seems the shipping would be insane.
Well, anyway, the microwave is still working, so I guess--health concerns aside--we're in the opposite place right now to Debt Free. When that goes--I don't know.