Similar to cars and bikes, having insurance is compulsory. Similar to the road going vehicles, there is a basic insurance for third party cover. There is also a passenger liability option, and hull cover (equivalent to Fully Comprehensive)
Costs vary, and will depend on aircraft, value, experience and previous claims.
Some companies will offer a no claims discount. The microlight forums have plenty of chat about who finds who best. As is the case in all insurance companies, you only really find out how good they are when you make a claim.
Here are some of the ones i have come across….