Ominously for the Republic of Ireland, the performances of Portugal in progressing to a semi-final meeting with France in Brussels tomorrow have been only marginally less impressive than the Dutch. With Portugal and the Netherlands in Ireland's World Cup qualifying group, the path could hardly look more arduous.
Unlike the other three countries still left in the competition, Portugal have never won a major title at senior level. Yet, with players like Luis Figo, Rui Costa, Nuno Gomes and Sergio Conceicao, they have the potential to seek out any lingering weaknesses in the make-up of world champions France.
Their form has again called into question the wisdom of Mick McCarthy's decision in agreeing to open his World Cup qualifying programme in Amsterdam on September 2nd and Lisbon five weeks later in what is surely the most difficult start of any in the competition.
McCarthy, here as a member of the BBC television team, insists that nothing of substance has changed over the last fortnight.
"We knew when we arranged the games that we were going in at the deep end," he said. "Of course, it's going to be tough, but I still believe that we can be competitive in both matches.
"Playing in front of a Lansdowne Road crowd, we're capable of beating anyone. And if we can nick a point against either the Dutch or the Portuguese, and win the other away games, we'll be there or thereabouts at the finish.
"Holland have been rightly praised for the type of football they've produced," he added. "But if anything, Portugal may be more dangerous for the simple reason that there is more movement in their team.
"At this point, however, I prefer to focus on our team and hope that by the time the new season starts, all the injuries which kept players out of the end-of-season games will have cleared."
McCarthy may find at least some solace in the lessons of history which show that teams which perform well in major championship finals in the summer don't necessarily carry that form into the new season.
Denmark, for example, failed to get out of Ireland's group for the 1994 World Cup finals after winning the European championship in Sweden two years earlier. And Croatia, undeniably, were suffering a hangover from their escapades in reaching the World Cup semi-finals in France two years ago when they came to Dublin two months later and lost 2-0.
To some, that may smack of whistling in the dark, but at this point it's as good a cause as any for sustenance as the Ireland players eye the prospect of being turned over by two of the best teams in the world.
Asked how he felt about competing in the Olympic Games at Sydney in September, Don Macey, the British decathlete, was honest enough to say: "terrified but excited". Those are the kind of sentiments, one suspects, that some of the Ireland players are likely to take with them on their early season travels.