I think there is no other way then using an oscilloscope for verify the output.
Some full graphic multimeters have basic oscilloscope functionality integrated which are good enough for check the wave from an DC-AC inverter.
Anyhow ... many appliances work just fine with mod-sine ways .. so pure sine waves are mainly needed for specific high power appliances.
In case of a mod-sine ways . .. in theory it is possible to apply a filter (for 10/20 USD) which can improve a bit the shape for the provided output wave