Bale swapped Tottenham for the Bernabeu in a deal which is believed to be worth a world record £85.3million - more than the £80million the Spanish club paid Manchester United for Ronaldo in 2009 - although full details of the fee have not been released.
There have been musings as to how the arrival of a player with a price tag to rival his own will affect Ronaldo's mood at Real Madrid, but his first chance to underline his worth comes when Portugal take on Northern Ireland in World Cup qualifying on Friday night.
It would not be unlike the mercurial 28-year-old to produce something special at Windsor Park, but O'Neill does not expect anything different from a player who has rarely suffered from a lack of self-belief.
Asked if Bale's signing created extra pressure on Ronaldo, O'Neill said: "I would doubt that extremely. He will regard himself as the best player in the world and he proves it every time he goes on the pitch.
"His aim is to prove that every time. He is a player who has the freedom of the pitch - he's not just a threat to whoever plays at right-back, he's a threat to the whole back four.
"It's not just a case of can we get someone to stifle him in that area of the pitch because he will just come to another area to get the ball."
O'Neill's side have previous form against Portugal, claiming a surprise 1-1 draw in Porto in the reverse fixture last October.
That night was supposed to be a celebration of Ronaldo's 100th cap but the party fell flat when Niall McGinn's goal ensured the unfancied visitors left with a point.
A similar result in Belfast would suit the hosts and O'Neill was unapologetic about the kind of game his team will have to produce to get it.
He has encouraged his side to play a passing style during his first campaign at the helm, but warned he would not be asking his men to go toe-to-toe with opposition ranked seventh in the world by FIFA.
"We don't want it to be a beautiful game of football if I'm 100% honest," he said.
"That's not how we're going to excel. They'd love the game to be open: they love space, they love to be able to play on the counter attack.
"It's important they have a difficult night and that they know from the word go that they're going to have a difficult night.
"I think it would be foolhardy of us to go and play a really open game and say to Portugal 'Come and play, you attack us and we'll attack you'.
O'Neill's plans for the match have been disrupted somewhat by a string of defensive withdrawals.
Three of the back four who helped defeat Russia 1-0 last month are absent, with Aaron Hughes (thigh) and Craig Cathcart (knee) injured and Daniel Lafferty suspended.
Ryan McGivern, who would have deputised at left-back for Lafferty, has also been ruled out with a knee problem meaning O'Neill must find alternative arrangements.
Alex Bruce and Rory McKeown are in the squad but boast just one cap between them, while Shane Ferguson and Corry Evans are both more comfortable in midfield.
It may, therefore, fall to the unattached Chris Baird, who flew in alongside Bradford's Rory McArdle as cover, to take on Ronaldo and company.
He has yet to sign for a club since his release by Fulham but has been training with QPR and has 61 international appearances to call on.
"We've got to be fair to the player, he's not had any competitive football since last season...but if I had to call on Chris I know he has got the know-how and the experience to be able to deal with it," said O'Neill.
"It's testament to him that given his contract situation he is willing to make himself available."