The 2008 European Commission fine -- a record at the time -- penalized Microsoft for failing to comply with the regulator's order four years earlier to provide information that would allow other products to work with computers running its software.
The software group has since taken a more conciliatory approach in dealing with the Commission, highlighted by its decision to reach a settlement with the regulator in 2009 when agreeing to let users of its Windows operating system choose their own browser.
Rival Google Inc has adopted a similar tone in handling an EU regulatory probe of its web search practices.
The fine was "most undeserved," Jean Francois Bellis, Microsoft's lawyer told the General Court, Europe's second-highest.
"This case would not have arisen if the Commission had been as explicit with respect to rates which it wanted Microsoft to charge as it had been with all other terms of licensing proposed by Microsoft," he said.
The Commission argued that Microsoft's actions after a 2007 court ruling showed that it was able to identify within a short time the measures needed to comply with its order.
"This is a case about a gambler who doubled up on a losing bet, lost again and now wants his money back," Nicholas Khan, a lawyer for the Commission, told the court.
The General Court typically gives its verdict between six months and just over a year after a hearing. Appeals can be lodged with the EU Court of Justice, Europe's highest court, but only on points of law.
The odds would appear to be in the Commission's favor, said Christian Riss-Madsen, a partner at law firm O'Melveny & Myers.
"I would think, based on its track record, the court would be reluctant to overrule the Commission's fining decision, giving the Commission some discretion in its enforcement," he said.
Still, it was possible the court could use the opportunity to issue a benchmark ruling that could set the direction for other abuse of dominant position cases coming up for judicial scrutiny, said Ramon Garcia Gallardo, a partner at SJ Berwin.
"Normally fine reductions in cartel fines have been relatively small. This case is important as it could show the court's approach on the Commission's position on high fines," he said.
The hearing will be watched by companies challenging regulatory fines, among them Intel Corp, which has appealed in EU courts against a 1.06 billion euro penalty imposed by the Commission last year.
Microsoft's non-compliance penalty was nearly double the original 497 million euro fine the Commission imposed on the company in 2004 for abusing its dominant position to thwart competitors.
Microsoft was supported in the case by the Computing Technology Industry Association and the Association for Competitive Technology.
IBM, Oracle Corp and Red Hat Inc were among seven parties who supported the Commission's position.
(Editing by Rex Merrifield and David Holmes) ($1= 0.7109 euro)