  We investigate in detail a family of quintessential inflation models in the
context of $R+R^2$ Palatini modified gravity. We find that successful inflation
and quintessence are obtained with an inflaton scalar potential that is
approximately quadratic in inflation and inverse quartic in quintessence. We
show that corrections for the kination period due to Palatini modified gravity
are subdominant, while the setup does not challenge constraints on modified
gravity from solar system observations and microscopic experiments, in contrast
to the metric case. We obtain concrete predictions regarding primordial
tensors, to be probed in the near future.
