It likely depends on how willing you are to modify your recipe. With a roux thickened sauce, I'm not sure how well it would translate to the microwave (though you're welcome to try, following Stephie's answer)
On the other hand, you can probably look for other thickeners - the point is, you need a thick liquid to melt your cheese into, and the thicker it is, the less likely your cheese is to clump up instead of melting smoothly. You could try using corn starch, that might work better (flour taste is more obvious when it isn't cooked enough, corn starch is more subtle).
Or you can try other thickeners - I've used a hot-water cheese sauce powder, just a spoonful to thicken which doesn't add a lot of flavor, since it's mild enough to be covered with the sharp cheese and other flavorings in the sauce. Or any other hot-water sauce powders that won't compete in flavor too much, maybe a touch of bullion powder, or instant gravy, or some such thing - just a little bit to thicken the milk, but the added flavor is mild over the whole recipe's volume. I've used mustard powder, or egg yolk powder, which both thicken a bit more in powder form - my version usually uses liquid mustard and egg yolk which help thicken and emulsify even wet, but while the yolk powder makes little difference other than extra thickening, but mustard powder is usually a lot spicier and less flavorful.
Sometimes I will mix a whole egg in, and stir often - the white firms up and ends up acting like a thickener, the yolk gives flavor and helps emulsify, though it helps that I don't mind the egg or the fact this can be somewhat lumpier, it tastes fine to me. Or I might start melting the cheese with the mustard and mushroom ketchup (which I use instead of Worcestershire sauce, similar flavor profile but I prefer it), and only add the egg yolk after, and milk a bit at a time once that's reasonably melted and mixed. For very sharp cheeses, it helps to let them sit in the milk for a while first, it hydrates them a bit more and lets them melt better.