Robson boosted the morale of the home crowd at SW19 on Tuesday when she defeated 10th seed Maria Kirilenko to be the only British woman to make the second round.
The victory meant Robson became the first British woman to beat a top-10 player at the All England Club since Smith overcame Conchita Martinez 15 years ago.
Smith then progressed to the fourth round - a feat that has not been matched by a home-grown player since.
Given that she has already dispatched Kirilenko, Robson is a big favourite to beat Mariana Duque-Marino on Thursday and then Peng Shuai in the third round.
"She has got the potential to go way further than the fourth round, whether it be this year or in the future," said Smith, who is working as a pundit for the BBC at this year's Championships.
"The worst thing she can do is look at the draw and think it has opened. There are still some pretty good names in there."
Robson has gone through a roller coaster 12 months since she claimed silver at the Olympics with Andy Murray.
The Australian-born star has defeated big names like Li Na, Kim Clijsters and Petra Kvitova this season, but she has struggled against some of the lesser-known players on tour.
Little is known about Duque-Marino, a qualifier from Bogota, but she did overcome 24-year-old German Julia Goerges in the previous round.
Smith hopes Robson does not take her opponent lightly.
"It will be different for her tomorrow compared to her first match," Smith said.
"Duque-Marino beat a very good player in the first round so she is obviously playing pretty well.
"It won't be just a shoo-in. Everyone thinks 'oh, it's just a qualifier from Colombia so it will be easy', but it won't."
Duque-Marino beat Goerges in a tight three-set encounter on Monday in what was her first appearance in the main draw at SW19.
The 23-year-old, who turned professional eight years ago, is 117th in the world.
Duque-Marino has never made it beyond the second round of a major, but she is hopeful of causing an upset.
"She (Robson) comes into the match after a good win, but I always think positive," Duque-Marino said.
"All I have to do is concentrate on my game and do everything well.
"It will be a hard game and I will have to play well to win it."
Robson admitted following her win over Kirilenko that she was nervous playing in front of a bumper crowd on Court One, where she won the junior championship five years ago.
Duque-Marino thinks the teenager will cope well with the pressure on her shoulders, though.
She added: "I think that she manages the pressure really well and it doesn't seem to affect her. She seems to play really well in front of a home crowd.
"She is a very, very good player, she hits the ball very hard and she's young. She is on an upward trajectory."
The match has been scheduled last on Court Two - the one on which Maria Sharapova and Caroline Wozniacki slipped and stumbled during their second-round exits on Thursday.
The game is likely to begin at around 1830 BST, giving her a prime-time TV audience that is likely to run into the millions.