And so, I am spending an inordinate amount of time at the moment, kneeling on the floor, peering. And I have discovered how to kill lots of them. Ha ha ha ha ha (maniacal laugh beloved of evil villains).
Step 1: To catch the easy ones... If you can see any of the red devils on the plant in question, quickly put your hand (or a piece of paper etc) underneath - if they see you coming, they will drop onto their backs on the floor, making them difficult to see. Having caught them in your outstretched hands, deal with them how you see fit. As an evil villain, I will naturally feed them to my subterranean pool of circling sharks.
Step 2. Some of the wee devils will be lurking around, trying to avoid looking as though they might be wanting to eat your fritillaries. They're difficult to see, sitting upside down in the undergrowth. So, shake the nearby vegetation. The lily beetles will drop to the floor. You may see one or two land, in which case deal with them how you see fit (perhaps subject them to decapitation using a butler with a sharp-edged bowler hat).
Step 3. Wait. Wait a little longer. But keep your eyes open. Soon, they will come. The dislodged devils will right themselves, and make their conspicuous way back towards the smell of their favourite food. And then you pounce. And then you deal with them how you see fit. By this point, I have had enough of devising evil genius-style methods of death (well, they always escape, don't they?). And so I crush them. Bwah hah ha hah ha haaaa.
Make sure you squish their eggs, too.