*759MEMORANDUM*

By separate order, we certify one issue in this case to the Supreme Court of California. In this Memorandum, we address the other issues, affirming in part, reversing in part, and remanding for further proceedings. Because the parties are familiar with the record, we will recite the facts only as necessary to explain our decision.

1. The district court was entitled to credit the testimony of Mr. Long and Mr. Sila that they did not expect high levels of catalyst to remain in Line B after the transfer of oil from Tank 147 to Tank 1072. See Anderson v. Bessemer City, 470 U.S. 564, 575, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985). Accordingly, the court properly found that Shell did not intentionally load contaminated fuel onto the Marin Tenor, and was not substantially certain that contamination of the Tenor would occur. We therefore affirm the district court’s conclusion that Shell did not commit an intentional trespass.

2. In calculating damages, the district court did not apply the liquidated demurrage rate of $400 per hour stipulated by Articles Three and Eleven of Marin Tug’s Schedule of Rates, Terms, and Conditions. Because the court’s decision declining to apply the stipulated rate was not fully explained, and because the court has not made factual findings adequate to support that decision, we remand for reconsideration of the appropriate measure of damages in accordance with the following principles.

“[T]he mere stipulation of a liquidated sum for demurrage [does not] obviat[e] the need to show actual damages.” Trans-Asiatic Oil, Ltd., S.A. v. Apex Oil Co., 804 F.2d 773, 782 (1st Cir. 1986). At the same time, “the requirement of proving actual damages does not vitiate the [stipulated] demurrage rate ... unless such a rate is so excessive that it constitutes a penalty.” Id. at 782 n. 9. So, where there is a stipulated demurrage rate, proof of some actual damages, while necessary, is only a threshold requirement, not determinative of the plaintiffs recovery.

We apply California law to determine the precise conditions that must be satisfied for a liquidated demurrage clause to be enforceable and to decide who bears the burden of demonstrating those conditions. “Admiralty courts, when invoked to protect rights rooted in state law, endeav- or to determine the issues in accordance with the substantive law of the State.” Hess v. United States, 361 U.S. 314, 319, 80 S.Ct. 341, 4 L.Ed.2d 305 (1960) (internal quotation marks omitted). Here, no federal maritime precedent is directly on point, and application of state law to this dispute would not frustrate the national interest in uniformity in admiralty law. All Underwriters v. Weisberg, 222 F.3d 1309, 1312 (11th Cir. 2000).

Citing Cook v. King Manor and Convalescent Hospital, 40 Cal.App.3d 782, 115 Cal.Rptr. 471 (1974), Westport and Shell would place on the Mudgetts “the burden of proving that, at the time the contract was entered into, it was in fact difficult or impracticable to determine actual damages in the event of breach, and that the contract amount represented a reasonable endeavor to ascertain and determine what the damages would be.” Brief for Appel-lees at 39-40.

Cook is of dubious precedential value because the underlying statutory provision, California Civil Code § 1671(b), was *760amended three years after Cook to express “a new general rule favoring the enforcement of liquidated damages provisions.” Law Rev. Comm. Comment, 1977 Amendment, 1985, Main Vol. at 497. Pursuant to the revised statute, a provision stipulating damages “is valid unless the party seeking to invalidate the provision establishes that the provision was unreasonable under the circumstances existing at the time the contract was made.” California Civil Code § 1671(b). Thus, Westport and Shell have the burden of proving that the contractual demurrage rate was unreasonable, and must do so not in light of the damages actually sustained, but in light of the parties’ reasonable expectations at the time the contract was entered into. On remand, the district court should reconsider the application of the contractual demur-rage rate in accord with these principles.

3. The district court should also reconsider on remand the period for which demurrage-liquidated or otherwise-is owed. The court declined to award demurrage beyond June 26, 1996, the date flushing of the Tenor was completed. The court made no finding, however, that Marin Tug learned the results of the flushing experiment on that date. The Mudgetts are entitled to demurrage for the period after June 26, 1996, until such time, to be determined by the district court, as Marin Tug was notified of Mr. Dedman’s conclusions.

4. We reject the Mudgetts’ contention that the district court erred by finding that flushing had adequately cleaned the Tenor. The Mudgetts’ challenge on appeal to the admissibility of Mr. Dedman’s testimony under Daubert v. Merrell Dow Pharm., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), was raised too late. Marbled Murrelet v. Babbitt, 83 F.3d 1060, 1066 (9th Cir. 1996). Moreover, the district court was entitled to credit the testimony other than Mr. Ded-man’s suggesting that flushing had successfully removed contaminant from the Tenor.

Even so, we cannot rule out the possibility that the Mudgetts ought to have been awarded damages to compensate them for the cleaning of the Tenor that occurred between August 1 and August 20, 1996. “[T]he consequences of an injury are recoverable where the injured party acts with such care and diligence as a person of ordinary prudence would under the circumstances, and his efforts to minimize damages are determined by the rules of common sense, good faith, and fair dealing.” Brandon & Tibbs v. George Kevorkian Accountancy Corp., 226 Cal.App.3d 442, 466, 277 Cal.Rptr. 40 (1990) (quoting 22 Am.Jur.2d, Damages, § 498, at 582-583). So the relevant question is not whether, viewed retrospectively, the further cleaning was unnecessary, but whether by cleaning the Tenor, Marin Tug acted with ordinary prudence under the circumstances as it reasonably understood them at the time. On remand, the district court should determine the availability of damages for the August cleaning under that standard.

AFFIRMED in part, REVERSED in part, and REMANDED for further proceedings.

Each party shall bear its own costs on appeal.