Veteran Kompany described Brazil as "individually ... the strongest team in this World Cup," during a media conference. But he said no Belgium players were "going to sleep at night thinking we have already lost to Brazil."
Kompany added that Belgium would look their "opponents in the eye" when they play at Kazan Arena in the pick of the quarter-finals in Russia.
Miranda, who will become the fourth Brazil player to wear the captain's armband at the tournament, said his opposing centre back was trying to pump his team up.
"We know all kinds of provocation, a way to hide your fear," Miranda said through a translator at the pre-match media conference on Thursday.
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"I think it’s a way of showing trust and hiding fear.
"You have to prepare yourself especially against the Brazil national team, and a leader like Kompany has to show confidence to his team mates, like the more experienced players have to show confidence in our actions to our team mates."
The match pits two of the most fancied teams at the World Cup, with Brazil's stingy defence to contend with Belgium's array of attacking threats.
Brazil have conceded just one goal in four matches, with Inter Milan's Miranda playing a big part in the defensive stonewall with centre back partner Thiago Silva.
The pair have started in all four games but may face their biggest test against a Belgian front line boasting the firepower of Romelu Lukaku and Eden Hazard.
Miranda said five-times champions Brazil could ill afford to focus on shutting down individual players, however, as they bid to reach a semi-final against either France or Uruguay.
"Belgium is not just Lukaku," he said.
"Certainly they have a very strong attack, but the main way to stop the opponent is to be aware of all the players on the pitch.
"(They have) several high quality players, they are very skilful and taller, so our defence will be very well-prepared to neutralise all of the opponent’s attacks."
(Reporting by Ian Ransom; Editing by Hugh Lawson)
