Wales last reached this stage of a major tournament at the 1958 World Cup, where their hopes were shattered by Brazil and a 17-year-old Pele, who scored the game's only goal in a 1-0 win.
Coleman's side will have the chance to go one better in Lille, where they will face a Belgium team among the favourites for the tournament after hitting top gear in a 4-0 win over Hungary in the last 16.
Coleman, however, says his players, who had endured several failed qualification campaigns before reaching Euro 2016, will not be feeling the strain with a best-ever tournament finish and a place in Welsh soccer history books up for grabs.
"We know what is at stake, it is a fantastic pressure to have, a positive pressure that we have earned," he told reporters on Thursday.
"We have experienced the other pressure (of being unsuccessful), which is tough, a lot tougher than this one we have got, I promise you that.
"We have to say since that 1958 quarter-final, you have to put this down as the biggest game our country's been involved in, which is a great place to be and a great pressure to have."
After an opening 2-0 defeat by Italy, Belgium have got into their stride, scoring eight goals in their next three matches, culminating in the rout of Hungary.
Their attacking players have found their feet, Eden Hazard in particular impressing with a stunning solo show against the Hungarians while Kevin De Bruyne and Romelu Lukaku have started to show what they are capable of.
"They will play with imagination," said Coleman. "They have got pace and power.
"But we will play how we play. When it is time to defend we will defend with our lives and when it is time to attack we will attack with our lives. If we do that Belgium will be in for a helluva game."
There had been fears that Wales captain Ashley Williams might miss the game after suffering a shoulder injury following a nasty collision with a team mate in their 1-0 last-16 win over Northern Ireland.
Having returned to training this week, Williams confirmed he was fine to start against Belgium.
"Obviously, it was hurting a lot at the end of the game and a lot of credit goes to the medical staff who have done a fantastic job. It will be fine for tomorrow," he said.
(Reporting by Toby Davis in Paris; editing by Ed Osmond)
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