I also think most reptile eggs are buried and guarded rather than sat on.
I am currently reading something that includes discussion of this. The dinosaur lines closely related to birds typically buried their eggs. Oviraptor dinosaurs in China (specifically, Heyuannia huangi) evolved open nests of the style now seen with the ratites (the long legged flightless birds like ostrich, emu etc.). Ratites and the tinamous incubate in large communal nests, some of which are incubated principally by the males btw (e.g. tinamou, rheas).This behaviour has also been documented in some birds, the megapodes. Most popular of those would probably be the Australian Bushturkey.
Crocodiles, alligators and gharials have a common ancestor with birds. Turtles are related one stage further back, while the lizards and snakes split off yet another stage back. Does anyone know, do they all bury their eggs? i.e. was it only the dinosaurs and birds that kept/developed nests above ground?