My better half found a set of silicone lids. Three in the set, about 6, 8 and 10 inches across. They are heavy enough to stay put, and make a reasonable seal, an sticky enough that they don't slide. Rinse after use, and leave by the microwave.
Another option: I've seen a cake cover type thing with a single 3/8" hole near the top. Place it over an open plate. This retains the steam, essentially acting as a lid. It also means you only wash the turn table.
If you are using a bowl to heat things, put a plate over the bowl. This may mean you need to use a larger bowl. Plate should normal side up. This is more stable, and drips go back to food instead of outside the bowl. This combination is awkward to pick up, especially if the plate is much larger than the bowl. An advantage is taht the plate can be a lid keeping food warm while waiting for the rest of supper.
For all of these, because steam is kept confined, the amount of time needed will drop, sometimes by as much as a factor of 2. Frozen veg with large chunks such as broccoli show a big time reduction.