Presumably some areas were occupied by Confederate troops, and thus couldn't send in their votes. How was this handled? Were there any proposals to cancel or postpone the elections?
Regarding the 1864 U.S Presidential Election:
Votes were cast by those in states that had not seceded or were not occupied. Soldiers could also vote, & they notably voted overwhelmingly for Lincoln. States such as Louisiana and Tennessee that had been retaken by American troops were granted electoral votes, which went to Lincoln.
Regarding the 1862 Midterms:
The seats of the south were considered vacant in the senate but as state legislatures selected senators the North had little problem with the senatorial election. I am fairly certain the aforementioned voting techniques were applied to House elections as well, in which the Democrats gained 27 seats and Speaker Galusha Grow lost his own re-election race.
1863 Confederate Congressional elections:
The Confederate elections took 6 months to process due to votes from Confederate soldiers and absentee ballots. “Refugees” from recaptured Union territory were able to vote here as well. No technical parties existed but a Pro Administration & an Anti Administration faction have been identified by historians.