Should I default to higher or lower power when the recommended power is not an option in a microwave?

Microwave ovens by their nature heat unevenly. The actual microwave radiation produces wave patterns with more and less amplitude within the cooking chamber. (From a physics standpoint, these are "standing waves" produced by internal wave reflections.) This is sort of the equivalent of "hot spots" and "cold spots" in a pan.

Most modern microwaves contain some sort of rotating plate or other moving part to mitigate this unevenness by keeping the food in motion (and thus aligning different parts of the food with the "hot spots"). Over time, some parts of the food will also become very hot, and the heat from those portions will gradually distribute to the cooler portions of the food around them.

The reason I bring all of this up is that the primary advantage to cooking at a "lower power setting" in a microwave (whether it truly can change wattage or whether it merely cycles between 100% power and off, as dpolitt's answer notes) is to allow time for those hotter portions of food to distribute their heat to the cooler portions during cooking.

If you're heating something that has easy heat circulation (e.g., boiling water or other thin liquids), it doesn't much matter what setting you use, so use higher power for time efficiency.

But in many foods using a lower setting can:

• Allow time for the food to heat more gradually and more evenly
• Prevent parts of the food from getting overcooked (which could lead to sections being dried out or otherwise changed to an overcooked texture)
• For longer cooking times, it may also allow the "cold spots" more time to "catch up" and spend more time at a cooking temperature, which may be desirable for texture (e.g., if the food has to soften) or other reasons
• Sometimes prevent undesirable "behavior" of food in the microwave when overheated: e.g., exploding or "popping" of some parts of the food, boiling over of some liquids, etc.

In general, I'd say that there's rarely much harm in using a lower cooking setting in a microwave, other than potentially wasting some energy. As long as you lengthen the cooking time to compensate and cook the food completely, a longer time is fine. So, that's what I'd recommend if you're at all concerned about the power setting.

The only time to avoid a lower power setting is generally in foods where longer cooking times would also be avoided in other cooking methods. For example, when steaming vegetables, a longer cooking time will often result in mushiness, which may be undesirable -- whether done in a pot on the stove or in a microwave on low power. (Some cooking requires a minimum temperature to achieve normal results too, like frying. In that case, you might need to use a higher power setting. I don't tend to use my microwave for such things, so I don't have a lot of recommendations for that.)

All of that said, the primary reason to use a microwave over other cooking methods is generally speed. That's why most people tend to just use full power on microwaves for the vast majority of tasks anyway. If you're heating a food where the things listed above are unlikely to pose a major problem, using higher power may be fine.

Lastly, in many foods interrupting cooking by periodic stirring is actually more effective to distribute heat evenly than a longer microwave time at lower power. Thus, I mostly tend to use a lower power setting myself only in foods that can't be stirred or where I don't want to be bothered to take the food out and stir periodically over a longer cooking time.

One way to approach the problem is to ask the question in a slightly different way: how do I generate the same amount of energy in a 750 Watt microwave that would be produced in a 850 Watt oven over four minutes?

Watts times time will give energy, and since we are not in a Chemistry or Physics forum, let's throw units out the window. 850 Watts times 4 minutes will give us 3400 units of energy (W min to be picky). To get the same amount of heat from a 750 Watt oven, solve the equation 750 * min = 3400 which is 4 minutes 32 seconds. In the 950 Watt oven that would be 3 minutes 35 seconds.

Since the power button on microwaves simply cycles the oven on and off (e.g. 80% does NOT mean that a 1000 Watt oven is operating at 800 Watt, but that it is only on 80% of the time), then we can include that in the equation as well for more general problems. So we have

WATT * time * power = energy

This equation should allow one to determine the time or % power to use to get the same amount of energy when cooking in an oven with a different power rating than the recipe calls for.

Most microwaves cannot modulate their power output. The power setting in those cases effectively just spreads out bursts of 100% power.

Unless you bought a microwave specifically with a feature marketed as something like inverter, accuwave, or optimawave it is unlikely that the power selection is doing much at all beyond taking more time. For more info on this topic see: Wikipedia - Pulse-width modulation.

In either case, microwaves can be very model specific in their performance so nothing really will beat trial and error for your own particular needs.