The authors of the constitution were extremely concerned with balancing power and particularly worâ­ried about limiting the power of the presidency. what are the two important ways they did it

Well, there are quite a few ways they limited the power of the presidency.

1) They gave Congress the power to override the presidency.
2) Congress also had the power to impeach.
3) Congress can deny presidential appointments.
4) Congress ratifies treaties.
5) Congress controls the declaration of war.
6) Congress also controls the budget.
7) The judicial branch (Court system) can rule presidential actions unconstitutional.
8) Judges appointed by the President sit for life - no getting rid of them if they make a decision the President doesn't like!

Hope this helps!