The gray matter will get a lot of action in such events. In this tradition, specially gifted scholars respond to a panel of experts from many subject areas with all in the panel allowed to ask any question any time. Poetry is always one of the subjects. The poetry expert in the panel would be asking the scholar on the stage to compose a poem, giving challenging conditions. For example, the first one may be giving a subject to start composing the poem.
Indian poetry has numerous meters and forms, probably more than any language in the world.
The tradition really started in Sanskrit with greatest poets of all time like Veda Vyaasa, Vaalmeeki and Kalidaasa. Mahabharatha is the longest poetry ever composed in the history. Surprisingly, even these poets did not develop the concepts of twin poems. They probably decided to leave this idea to be developed after few millenniums by a very ordinary man like me. We can employ many techniques to present twin poems in a public poetry reading.