For the past year, newspapers and magazines have been full of stories about how the tightening market for liability insurance has presented major problems for chemical companies or sporting-goods manufacturers or midwives. But another group squeezed by the sudden reluctance to insure risky enterprises has been those very newspapers and magazines themselves. Libel insurance has become hard to find and, when it is available, restrictive and expensive.

Much of the reason for the sudden change has little to do with what is actually happening in libel law. When interest rates were high, insurance companies ran after almost any business to get premium income to invest. Now that those rates have plummeted, insurers have begun to look a lot more seriously at just what sort of risks they really want to cover. But the increasing willingness of disgruntled newsmakers to go to court to challenge stories they do not like clearly has worsened the situation for media-insurance buyers. The Sharon, Westmoreland, Falwell and Tavoulareas cases made the headlines, but even more worrisome to media managers are dozens of other cases that are not as newsworthy, but that frighten off potential insurers.

Ann L. Heavner, an assistant vice president of Johnson & Higgins, the big insurance brokerage, pointed out to a Practicing Law Institute seminar on the problem that the three Lloyd's of London syndicates serving media clients have stopped accepting new business. Such U.S. underwriters as Chubb and American International Group have gotten very picky about issuing such policies, she said. And when existing contracts are renewed, "newspapers, publishing houses and television and radio stations are being presented with premium increases ranging from 25 percent to 200 percent, along with higher deductibles, severely reduced coverage terms, and sometimes participation clauses as high as 20 percent," she said.

James C. Goodale, a New York City libel lawyer, tells of one group of newspapers in the Southwest that saw its libel insurance premiums rise from $7,700 two years ago to $13,900 last year and $31,872 this year. At the same time, the deductible -- the amount of any libel loss that the papers have to pay -- rose from $20,000 to $25,000. And Goodale predicts that both premiums and the deductible will continue to rise.

It's not that broadcasters and publishers are doing so poorly in the courtroom. The Libel Defense Resource Center did a study in 1982 that showed plaintiffs winning 87 percent of the verdicts in cases that actually went to trial; follow-up reports in 1984 and 1985 show that win rate fell to below 60 percent. The win rate was sliced considerably when a case was appealed: In none of the three studies were more than 40 percent of the verdicts for the plaintiffs upheld by a higher court. And while million-dollar verd cts at trial have become relatively common, the resource center's research shows that not a single such massive award was upheld at the appellate level. In fact, any award of above $500,000 was either reduced or tossed out entirely.

Insurers, of course, do not like facing the threat of having to pay out such damages. But what distresses them even more is the virtual certainty of having to pay huge legal bills to defend customers against such charges, even if the defense is successful. "These attorneys' fees, rather than large damage awards, are the insurers' major cost," Goodale notes. He says that insurance companies tell him it is "not uncommon" for the defense bill in a run-of-the-mill libel case to come to close to $300,000, with about 80 percent of that total made up of the lawyers' bill for their time, and the rest for administrative expenses plus any money actually paid out in settlement.

One response has been a new kind of insurance policy in which the insurer covers most of any payment that has to be made to a defendant, but leaves it up to the broadcaster or publisher to pick up the bulk of the defense costs. "Many, if not most, of the large city dailies are only insurable with very large deductibles of where the insured will pay their own legal expense," Larry Worrall, president of Media/Professional Insurance Inc., told the Practicing Law Institute gathering. In return, media managers have shown more interest in capping legal costs; The New York Times, for instance, sends its lawyers a set of guidelines that say the paper will not pay for first-class travel, for the time a law firm spends drawing up a bill, or for expenses that are over the amount initially budgeted for the particular case.

The insurance business tends to be more cyclical than most, and the current difficulty that publishers and broadcasters are having getting libel insurance is a direct response to the easy standards and low rates of the recent past. By the middle of 1987, Heavner expects to see "the commercial insurance pendulum beginning to swing toward market softening." That's some comfort, but not much, to the executives who have to okay tomorrow's edition.