In 1998, Gates appeared before Congress alongside ex-Sun Microsystems CEO Scott McNealy and former Netscape CEO Jim Barksdale to address concerns over Microsoft’s (MSFT) stranglehold on the computer operating system market. (At the time, Microsoft’s Windows platform could be found on at least 90% of all personal computers.) Schmidt is in, if not the same, a similar boat. As the leading U.S. search provider, Google (GOOG) powers 65% of Internet searches domestically, a position that came under fire recently when companies like Yelp and Expedia Inc. (EXPE) accused the Internet giant of prioritizing its own services in search results over Yelp’s and Expedia’s. If true, such a move could be judged monopolistic.

According to The Wall Street Journal, Google is doing all it can to put its best face forward, including hiring some 13 lobbying and communications firms to stump on its behalf. Only time will tell, whether today’s hearings lead to more robust government action. What’s certain is that Schmidt could glom a few vital lessons from Gates’ appearance:

Don’t sweat it.
Throughout 1998’s four-hour-plus hearing, Gates held his own, fielding argumentative questions and scathing criticism. (Phrases like “predatory practices” were liberally bandied about by questioners.) And while overall the appearance earned mixed reviews, Gates appeared confident throughout. It may be the most elementary lesson in courtroom basics but, for Schmidt, appearing confident and composed will be key. After all, nothing quite screams “ untrustworthy” like meek responses, nervous ticks or a sweaty brow.

Don’t get carried away.
Gates had every right to be proud of his achievements with Windows and Office, which propelled Microsoft’s value into the stratosphere during the late-1990s. Senator Orrin Hatch even acknowledged as much in his criticism, describing Microsoft’s growth as “breathtaking.” But Gates probably should have still checked his swagger at the door. When Senator Ted Kennedy referred to recent statements made by then-Microsoft COO Bob Herbold, Microsoft’s CEO flippantly responded. “When I decided to create Microsoft, I did not call up IBM (IBM) to say: ‘IBM, do you think there’s any chance for me to create an operating system and sell hundreds of millions of copies,’” Gates began. “So when you ask Mr. Herbold should you take on Microsoft head on and create a new operating system, if that’s how you’re going to decide whether to do it, I’d suggest you’re not the kind of entrepreneur that’s going to make that happen.” Ouch.

Thoughtful and often soft-spoken, Schmidt isn’t likely to go so operatic. He has, however, made statements in the past that have been — while honest — total public relations distaters. (He told The Atlantic, for example, that his company’s privacy policy consisted of getting “right up to the creepy line and not cross it.“)

Don’t mince words.
It’s one thing to emphatically deny monopolistic practices. But deflect questions about your market dominance — something obvious to everyone in the room — doesn’t help. Such was the case with Gates, who said Microsoft’s success couldn’t be contributed to any one product. In fact, Gates’ responses in general seemed purposely vague, to the point where Senator Hatch grew exasperated and at one time described Gates as “somewhat hard to nail down on a very specific question.” As with any testimony or deposition, being direct will be key for Schmidt. Not only will he be respected as a straight shooter — regardless of the content of his responses — he’ll save everyone’s time in the process.

Don’t be rude.
Gates’ performance during the hearing didn’t sway the powers that be. Two months later, Microsoft was slapped with an antitrust suit, a filing that would plague the company for years even if it eventually came out on top.

In November 1998, a 50-minute segment from a three-day taped deposition Gates gave, was shown during Microsoft’s antitrust trial. In it, he antagonized U.S. Justice Department attorney David Boies, correcting him on the alleged differences between a “memorandum” and an email, asking for prior questions to be restated and instructing Boies — not always civil himself — on how to do his job better. Needless to say, Gates’ behavior didn’t make an admirer out of the judge, who ordered Microsoft a year later to break up into two separate units. (That ruling was eventually overturned.)

While this week’s hearing doesn’t necessarily precede an antitrust trial similar to Microsoft’s, Google’s executive chairman would do well to remember Gates’ less-than-stellar deposition, too. Because as Gates eventually realized, being a hostile witness won’t do much more than draw out legal proceedings — and not necessarily in his favor.