This is a really simple idea on the surface. I just wrote up my thought process to explain why it should work well.
There are compromises for everything in life -- you can't have it all. I love the speed of microwave, but don't like the results. I love the juiciness & tenderness from slow roasting, but want something faster.
.....what if we could get the benefits from both methods?
We start with meat from the fridge at around 40F and I like to finish at 130-145F (rare to medium/medium-rare). We have roughly a 100F difference from start to finish. Physiological temperature is around 100-102F for most livestock. We know that it naturally exists at that temperature and so anything at that temperature or below will not exhibit any "cooked" qualities. In fact, we know that collagen in meat doesn't break down into gelatin until 120F. So both methods, in theory, should produce similar quality until 120F. From 120F on, the meat cooked in the oven is far superior.
You can heat meat in the microwave and get it to 100F using a rough formula of 1-2 min/lb on high power. You may have to experiment with your microwave to see what setting/cooking time works best for you and depending on the cut of meat/surface area. Transfer the meat to an oven and finish it off. Depending on the thickness and shape of the meat and type of microwave, there could be a lot of variation so try it out and see what works for you.
Afterwards, insert a meat thermometer and measure the temp. Keep microwaving until it gets to about 100F in the core. The outer edge could turn a bit brown and that's ok. I really like using the kind below. They go for about $13 at Walmart and you can place the probe in the meat while in the oven and monitor the display on the outside as it roasts in the oven.
I am planning on posting a tri tip recipe soon using this method to illustrate it's use. It works best for cuts like tri tip because it's flat. Thick, round cuts are harder to heat in the center. I found that I cut my cooking time in half with just a few minutes of work.