Spades - Strategy for Nil Vs. Nil round
Some of the strategy will depend on the bids of the non-nil players.  In Suicide Spades, the non-nil players must have each bid at least 4, but that could still be anything between 4 and 13.  A bid of nil is equivalent to a bid of 10 in terms of points (100 if you win, -100 if you lose), so a non-nil player who has bid in the realm of 10 is as concerned with making their bid they are with protecting their partner's nil bid.  Meanwhile, a player who has bid in the realm of 5 is much more concerned with protecting their nil bid partner.  Bags are also a concern, as bags are worth up to -10 points each.

For the sake of the rest of the discussion, let's call the players A, B, C, and D, where B and C are the ones who made the nil bids, so A and D are leading rounds after the first (unless one of B or C takes a trick).  Here are some specific considerations:


D has the benefit of going last in some rounds, which A never has.  Thus, D should keep some low cards to be able to capitalize on the situation where C has played the highest card.
C has the benefit of playing after B each round, and thus can play the highest card still covered by B each round.  This positional benefit may rival D's.
A and D, by leading far more often than usual, have a much easier time getting a void in a suit, and probably want to do so, as this allows them to use a spade on that suit or lead spades to allow their partner to get rid of any spades.  The risk of this is if they lead a low card, one of the two nil players is more likely to take the trick, but it's not necessarily clear which.
It is especially important for A to get a void if A wants to lead spades, as D can reduce A's options by not breaking spades.
If either of A or D knows that their partner has a void in a suit, they should definitely lead low in that suit, as this has a decent chance of forcing the other nil bid player to take the trick.
If you are playing suicide spades, or are playing regular spades and two players have already made nil bids, you may want to bid several higher than you were originally planning, as multiple players will be actively avoiding taking tricks.