Taxa closer to Reptilia
(e.g. Silvanerpeton) than to Lissamphibia (e.g. Rana) are considered Reptilomorpha by definition (Säve-Söderbergh 1934). Contra tradition and paradigm (see below), in the large reptile tree (LRT, 1440 taxa) most of the following taxa (Fig. 1) are basal (non-reptle) taxa that fulfill this definition. Some outgroup taxa are also shown along with Silvanerpeton, the last common ancestor of all reptiles (= amniotes) in the LRT.

Figure 1. Members of the Reptilomorpha. starting with Caerorhachis and their proximal outgroups illustrated to scale and in their phylogenetic order from top (primitive) to bottom (derived). Not all reptilomrophs have long limbs and large feet, but these traits are generally not found in non-reptilomorphs. Frogs are important convergent exceptions.
The clade Reptilomorpha
includes all members of the clade Reptilia (= Amniota), but we’re going to focus on the stem amniotes today, basically from Caerorhachis to Gephyrostegus.
According to Wikipedia
“As the exact phylogenetic position of Lissamphibia within Tetrapoda remains uncertain, it also remains controversial which fossil tetrapods are more closely related to amniotes than to lissamphibians, and thus, which ones of them were reptiliomorphs in any meaning of the word. These include the diadectomorphs, seymouriamorphs, most or all “lepospondyls”, gephyrostegids, and possibly the embolomeres and chroniosuchians. In addition, several “anthracosaur” genera of uncertain taxonomic placement would also probably qualify as reptiliomorphs, including Solenodonsaurus, Eldeceeon, Silvanerpeton, and Casineria.”
Most of these taxa
nest within the clade Reptilia in the LRT. Taxon exclusion has been the traditional cause of this problem, something the LRT was designed to take care of with high confidence because all candidates are tested.
Origin of amniotes
Wikipedia reports, “Exactly where the border between reptile-like amphibians (non-amniote reptiliomorphs) and amniotes lies will probably never be known, as the reproductive structures involved fossilize poorly, but various small, advanced reptiliomorphs have been suggested as the first true amniotes, including Solenodonsaurus, Casineria and Westlothiana.”
In the LRT, these three taxa nest well within the Reptilia.
Exactly where the last common ancestor of all living reptiles has been known for several years. Phylogenetic analysis makes this easy. Whichever taxon is the last common ancestor all living mammals, birds, lizards and crocodilians marks the border. Here in the LRT, that taxon is Silvanerpeton (Fig. 1) from the Viséan (Early Carboniferous) with an even earlier genesis because several reptile ingroup taxa are coeval in the Viséan.

Figure 1. Subset of the LRT focusing on basal tetrapods and showing those taxa with lobefins (fins) and those with fingers and toes (feet). Inbetween we have no data. By this cladogram and by definition, Microsauria is a clade within Reptilomorpha.
Not all reptilomrophs have long limbs and large feet,
but these traits are generally not found in non-reptilomorph basal tetrapods. By convergence, frogs (genus: Rana) are important exceptions. Needless to say, longer, stronger limbs are ideal for terrestrial excursions, despite the fact that some reptiles, like snakes and skinks, get along very well without them.
Earlier we talked about the lack of posterior dorsal ribs in the earliest reptiles. This provided additional space for gravid females to grow amniotic eggs prior to laying them. A deep pelvis permitted the expulsion of larger eggs. A deeper pelvis is found in Eusauropleura (Fig. 1) and more derived taxa. Platyrhinops (Fig. 1), in this regard a reptile-mimic, also had a deep pelvis and long legs by convergence.
The earliest fishapods,
like Panderichthys and Tiktaalik had a wide flat body with dorsal ribs that were much wider than deep — less chance for tipping while walking. This wide, flat morphology is retained up to Utegenia, when the dorsal ribs start curving to enclose a deeper, narrower torso (by convergence with other taxa, like Ichthyostega. At the same time the orbits moved laterally.
Not all reptilomorphs are small,
but the earliest reptilomorphs were no larger than than the juveniles of their ancestor, Greererpeton (Fig. 1), distinct from the giant ‘amphibians’ we looked at earlier.
References
Carroll RL 1991. The origin of reptiles. Pp. 331–53 in Schultze H-P and Trueb L editors. Origins of the higher groups of tetrapods — controversy and consensus. Ithaca: Cornell University Press.
Gauthier J, Kluge AG and Rowe T 1988. The early evolution of the Amniota. In The Phylogeny and Classification of the Tetrapods: Volume 1: Amphibians, Reptiles, Birds. Edited by MJ Benton. Clarendon Press, Oxford, pp. 103–155.
Ruta M, Coates MI and Quicke DLJ 2003. Early tetrapod relationships revisited. Biological Reviews 78 (2): 251–345.
Säve-Söderbergh G 1934. Some points of view concerning the evolution of the vertebrates and the classification of this group. Arkiv för Zoologi. 26A: 1–20.