Low bandwidth Pr-based cobalt perovskites, such as Pr${}_{1\ensuremath{-}x}$Ca${}_{x}$CoO${}_{3\ensuremath{-}\ensuremath{\delta}}$, have received significant recent attention as they undergo first-order spin-state transitions with a strong influence on magnetic and transport properties. The unique nature of the Pr-O bond has been implicated as the impetus for these transitions, as it is thought that temperature-dependent charge transfer can occur between Pr and Co ions, i.e., a partial Pr${}^{3+}$\ensuremath{\rightarrow}Pr${}^{4+}$ and Co${}^{4+}$\ensuremath{\rightarrow}Co${}^{3+}$ valence shift. In the present work, we have studied the related compound Nd${}_{1\ensuremath{-}x}$Ca${}_{x}$CoO${}_{3\ensuremath{-}\ensuremath{\delta}}$. The Nd${}^{3+}$ ions have very similar ionic radius to Pr${}^{3+}$ but do not induce a temperature-dependent valence shift (at least in the composition range studied here), enabling deconvolution of the intrinsic low bandwidth physics from the unique effects of Pr-O bonding in Pr${}_{1\ensuremath{-}x}$Ca${}_{x}$CoO${}_{3\ensuremath{-}\ensuremath{\delta}}$. To this end, we have characterized the structural, magnetic, and electronic transport characteristics of Nd${}_{1\ensuremath{-}x}$Ca${}_{x}$CoO${}_{3\ensuremath{-}\ensuremath{\delta}}$ bulk polycrystals, using neutron diffraction, small-angle neutron scattering, dc and ac magnetometry, and magnetotransport, and have established the Nd${}_{1\ensuremath{-}x}$Ca${}_{x}$CoO${}_{3\ensuremath{-}\ensuremath{\delta}}$ magnetic phase diagram. This phase diagram contains regimes of short-range ferromagnetism and long-range ferromagnetism, in addition to ferrimagnetism. We argue that, with the exception of the valence transition that occurs at high $x$ (e.g., $x$ $=$ 0.5) in Pr${}_{1\ensuremath{-}x}$Ca${}_{x}$CoO${}_{3\ensuremath{-}\ensuremath{\delta}}$ and the low-temperature ordering of Nd${}^{3+}$moments that results in the ferrimagnetism in Nd${}_{1\ensuremath{-}x}$Ca${}_{x}$CoO${}_{3\ensuremath{-}\ensuremath{\delta}}$, the two systems are nearly isostructural and have similar magnetic and transport properties. The low bandwidth physics intrinsic to both systems is summarized as encompassing long-range ferromagnetism with a relatively low Curie temperature due to Co-O-Co bond buckling (60 K for Nd${}_{1\ensuremath{-}x}$Ca${}_{x}$CoO${}_{3\ensuremath{-}\ensuremath{\delta}}$), short-range ferromagnetism that emerges at much higher temperatures (\ensuremath{\sim}270 K for Nd${}_{1\ensuremath{-}x}$Ca${}_{x}$CoO${}_{3\ensuremath{-}\ensuremath{\delta}}$), and likely stems from oxygen deficiency, exchange-spring behavior related to magnetoelectronic phase separation, and a doping-driven insulator-metal transition. In addition to elucidating the essential physics of narrow bandwidth perovskite cobaltites, the results thus further confirm the importance of the unique features of the Pr-O bond in driving the abrupt spin-state transition in Pr${}_{1\ensuremath{-}x}$Ca${}_{x}$CoO${}_{3\ensuremath{-}\ensuremath{\delta}}$.