  The prime Kepler mission revealed that small planets (<4 R_earth) are common,
especially around low-mass M dwarfs. K2, the re-purposed Kepler mission,
continues this exploration of small planets around small stars. Here we combine
K2 photometry with spectroscopy, adaptive optics imaging, and archival survey
images to analyze two small planets orbiting the nearby, field age, M dwarfs
K2-26 (EPIC 202083828) and K2-9. K2-26 is an M1.0 +/- 0.5 dwarf at 93 +/- 7 pc
from K2 Campaign 0. We validate its 14.5665 d period planet and estimate a
radius of 2.67^+0.46_-0.42 R_earth. K2-9 is an M2.5 +/- 0.5 dwarf at 110 +/- 12
pc from K2 Campaign 1. K2-9b was first identified by Montet et al. 2015; here
we present spectra and adaptive optics imaging of the host star and
independently validate and characterize the planet. Our analyses indicate K2-9b
is a 2.25^+0.53_-0.96 R_earth planet with a 18.4498 d period. K2-26b exhibits a
transit duration that is too long to be consistent with a circular orbit given
the measured stellar radius. Thus, the long transits are likely due to the
photoeccentric effect and our transit fits hint at an eccentric orbit. Both
planets receive low incident flux from their host stars and have estimated
equilibrium temperatures <500 K. K2-9b may receive approximately Earth-like
insolation. However, its host star exhibits strong GALEX UV emission which
could affect any atmosphere it harbors. K2-26b and K2-9b are representatives of
a poorly studied class of small planets with cool temperatures that have radii
intermediate to Earth and Neptune. Future study of these systems can provide
key insight into trends in bulk composition and atmospheric properties at the
transition from silicate dominated to volatile rich bodies.
