Typically you can take your time to set up against this match, land an early Liliana of the Veil, with counter-backup, and attempt to kill once the path is clear. You might even wait a turn after taking a look at their hand with Thoughtseize. Now that Sensei’s Divining Top is banned, and Counterbalance is less prevalent, your biggest concern is Jace, the Mind Sculptor, and an unchecked Monastery Mentor.
Save Stifle for critical fetchlands, planeswalker activations (Jace ultimate), and miracle triggers.
If they are playing non-basic lands, attack Tundras and Search for Azcanta with Wasteland if you are on the Marit Lage plan. If you are on the Jace, the Mind Sculptor plan, then take out the Volcanic Islands and be on the look-out for Pyroblast & Red Elemental Blast.
When sideboarding, leave in some hand disruption, and some countermagic so you can protect Marit Lage or Jace, the Mind Sculptor when it comes time to actually try to win the game. They will sometimes sideboard out Counterbalance and bring in more win conditions like Monastery Mentor, and bring in more Pyroblasts to deal with Jace.
I recommend at least one Garruk Relentless and one Liliana, the Last Hope in the sideboard. These provide non-blue win-conditions that are difficult to remove and provide consistent pressure against Miracles’ endless stream of removal.
Some Miracles lists also run Blood Moon in the sideboard, so be sure to fetch enough basics lands to cast Abrupt Decay.