There's really two philosophies when approaching these matchups, it comes down to if they have lock pieces or not (along with what game it is). In game one against Miracles, they have tons of cards in their deck that interact poorly with you (Swords to Plowshares, Terminus, Jace, the Mind Sculptor), because of this and Counterbalance it's best to kill them as quickly as possible - while playing around Force of Will.
If you're able to keep Counterbalance off-line or in a control matchup without it, you're able to grind them down with Past in Flames. There's access to a main deck copy and then the sideboard copy can be retrieved with Burning Wish. The goal is to get the opponent to spend resources while you 2-for-1 them, when they have some dead draws in their deck. What I don't recommend is going for Empty the Warrens against Miracles, mainly due to Terminus. That said, Engineered Explosives has become popular due to Chalice of the Void - which provides another answer for Goblin tokens.
It's important to keep in mind, how the opponent is trying to combat you. Sensei's Divining Top is often going to keep a Force of Will or Counterspell on top of their deck, this way discard spells can't stop their plans.
In post-board games, it's better to slow the game down as that is what the opponent is trying to do as well. It's best to side out copies of Chrome Mox as it's inherently a faster card since its card disadvantage at the cost of the mana it provides – meaning over a longer game that its less valuable. It also doesn't help with the game plan of using Past in Flames as a means of card advantage. It's important to keep in mind that these decks are likely siding in Flusterstorm, which can be problematic, especially if you're going for the natural storm kill with Tendrils of Agony in hand. That said, if they don't have Flusterstorm, you've likely won the game.
For more information on how to beat Miracles, please read AJ Kerrigan's article linked below.
Non-miracles control decks – I suggest siding out Empty the Warrens as most decks have answers in Golgari Charm, Toxic Deluge, Batterskull, Engineered Explosives and plenty of other cards. The Tendrils of Agony from the sideboard will get you a lot farther against these decks as you likely have enough time to build into a high storm-count.
For matchups with Meddling Mage I bring in Abrupt Decay, Grapeshot or Tendrils of Agony. These help off set the effectiveness of Meddling Mage forcing us into awkward situations where we're forced into casting Empty the Warrens.
Copies of Ponder are usually sided out against Miracles as a way to find room, TES doesn't have a lot of "flex spots" and Miracles is known to bring in up to three copies of Pyroblast. This limits their effectiveness against TES. Sideboarding for this matchup can be difficult as there are so many cards we would like to bring in, but the entire deck feels useful in some way.
Surgical Extraction can be used in a number of ways: the most obvious is in response to Snapcaster Mage targeting something useful, there's also removing all the copies of Counterbalance, Force of Will or Flusterstorm from the game. I think the best use is as a shuffle effect in response to your opponent drawing a card with Sensei's Divining Top in an attempt to counter a key spell on the stack.
03-18-2017 Bryant Cook vs. Joe Stempo with bUrg Midrange at Eternal Extravaganza VI: Washington, DC
08-04-2016 Fighting the Miracles Menace by AJ Kerrigan on theepicstorm.com
04-22-2016 Steven Fierro vs. Fred Chen with Deathblade at Fire & Dice in Woodland Hills, CA
09-04-2015 Xantid Swarm Vs. The Metagame by Bryant Cook on theepicstorm.com
08-22-2015 Joey Valente vs. Corey Armstrong with Shardless BUG at Fire & Dice in Woodland Hills, CA
08-11-2015 Jordon Robbins vs. Jon Ha with Miracles at Ready to Play Trading Cards in Columbia, SC
01-10-2015 Bryant Cook vs. Zane Knapp with Esper Deathblade at StarCityGames: Philadelphia, PA
08-10-2014 Bryant Cook vs. Lloyd Kurth with Shardless BUG at StarCityGames: Syracuse, NY
06-13-2014 Bryant Cook vs. Reid Duke with Miracles at StarCityGames Invitational: Columbus, OH
08-27-2013 Bryant Cook vs. Harry Corvece with Shardless BUG at StarCityGames: Baltimore, MD
06-23-2013 Matthew Bevenour vs. Brad Nelson with Esper Deathblade at StarCityGames: Philadelphia, PA
03-17-2013 Bryant Cook vs. JD Nir with Esper Stoneblade at StarCityGames: Washington, DC
05-12-2012 Bryant Cook vs. Sam Roukas with BUG Control at Jupiter Games in Binghamton, NY
02-11-2012 Bryant Cook vs. Tariq White with Stoneblade at Jupiter Games in Binghamton, NY