  We determine the current-phase relation (CPR) of two-terminal configurations
of Josephson junctions containing two-dimensional (2D) time-reversal invariant
topological superconductors (TRITOPS), including TRITOPS-TRITOPS, as well as
junctions between topological and non-topological superconductors (TRITOPS-S).
We focus on long junctions for which several channels intervene in the
tunneling coupling through the junction. We present a description of the
topological edge modes for different TRITOPS models including $p$-wave pairing
and the combination of $s$-wave pairing with spin-orbit coupling. We derive
effective low-energy Hamiltonians to describe the Josephson junction, which can
be solved analytically to explain the contribution of the edge states to the
Josephson current as a function of the phase bias. We find that edge-modes
yield singular corrections to the CPR for both junction types. The primary
effects occur for the response of the Majorana zero-modes at half-flux quantum
phase $\phi\approx \pi$ in TRITOPS-TRITOPS junctions and for integer flux
quantum phase $\phi \approx 0$ for TRITOPS-S junctions, respectively. The
former effect is particularly strong two-component nematic superconductors. The
latter effect leads to a spontaneously broken time-reversal symmetry in the
TRITOPS-S junction and to a breakdown of the bulk-boundary correspondence.
