Judge Royce Lamberth of the US District Court for the District of Columbia said on Thursday Iran should give $13 million in compensatory damages and $300 million in punitive damages to the four children of Leah Stern.
Stern was killed, at the age of 69, in an operation carried out by Hamas, the leading Palestinian resistance group.
She was among 15 people killed in the attack, which caused injuries to about 168 others.
Stern was badly burned and sustained severe injuries. The blast removed much of the skin from her face and cut her abdomen, exposing her intestines.
According to court documents, doctors said she had suffered at least several minutes from her wounds before dying.
Lamberth said that Stern's sons Shaul Stern, Joseph Stern and Shimson Stern and daughter Yocheved Kushner provided "clear and convincing evidence" to back up their claims in the case.
They said that the Iranian government has trained and funded Hamas to carry out attacks against Israel and the West.
US State Department spokesman, Richard Boucher, said that such plaintiffs could ask courts to give them legal claim to frozen Iranian assets.
He said the US government allocates partial compensation in such judgements to needy plaintiffs pending the rulings.
"The current system is based solely on litigation," Boucher told a press briefing, highlighting the numerous other cases against Iran and other countries.
He said that many victims were left with nothing but large default judgements.
“And so we have seen many cases where victims have obtained judgements attempting to attach blocked assets, and then they have to compete against each other for satisfaction against the very same assets."
The US State Department has included Iran on its list of state sponsors of terrorism.
Court documents said that the Iranian government’s support for what was referred to as “terrorism” was an official state policy and that such support went primarily through the Ministry of Information and Security (MOIS).
The documents alleged that Iran’s supreme leader, Ayatollah Ali Khamenei and other high-ranking officials, such as, Ali Akbar Hashemi Rafsanjani and Ali Fallahian-Khuzestani had approved MOIS support for Hamas.
The three political figures were named as defendants in the legal case filed in October 2000, along with the Iranian government and the country's Ministry of Information and Security.
The judge considered the bombing attack, in which Stern was killed, an "extra-judicial killing".
"Iran and the MOIS provided 'material support or resources' to Hamas and its operatives ... for the specific purpose of carrying out such acts of extra-judicial killing," the judge said.
Lamberth also noted that the family members' testimony "compellingly demonstrates how from the day of the bombing onward, the lives they had previously led had been irrevocably shattered."
The judge praised Stern's children for filing the suit, saying they had exerted “efforts to do something to deter more tragic deaths and suffering of innocent Americans at the hands of these terrorists."