When Apple sued Samsung for patent infringement more than five years ago, it kickstarted a wave of contentious litigation that quickly spread across a number of legal jurisdictions across the globe. In the process, a treasure trove of Apple secrets were revealed as Apple spared no expense as it tirelessly fought to hold Samsung accountable for ripping of the look and feel of both the iPhone and the iPad.

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Ultimately, Apple’s patent battle with Samsung was a successful endeavor, with a jury initially deciding that Samsung owes Apple a little more than a billion. Over the past few years, various updates and rulings have lessened that amount considerably. As it stands today, there’s no question that Samsung will have to open up its wallet and hand over some serious cash to Apple. What remains unknown, however, is just how much Samsung will be on the hook for.

Looking to settle things once and for all, Apple and Samsung tomorrow will head to the U.S. Supreme Court where they will both plead their respective cases. Specifically, the two companies will argue just how much out of a $548 million judgement Samsung will have to pay Apple. At the very least, Samsung will pay Apple $149 million. That said, the two companies have opposing views when it comes to how much of the remaining $399 million should be paid.

In broad terms, the arguments each side will put forward will be extremely familiar. Apple will argue that Samsung willfully infringed upon its design patents and that letting them off the hook will only serve to lessen the protections afforded to patent holders, thereby lessening the incentive for companies to innovate. Samsung, meanwhile, will argue that Apple shouldn’t enjoy patent protection for items that are obvious in nature.

More specifically, Samsung will argue that the $399 million in damages – itself based on patent infringement from a handful of ancient Samsung devices such as the Galaxy S2 and the Samsung Infuse 4G – is far too excessive.

CNET, which has a really comprehensive piece about what we can expect to see tomorrow adds:

Samsung believes design patents are given too much value when it comes to legal damages. The company contends that Apple should get profits only from the parts of a smartphone that infringe Apple’s patents — the front face and a grid of icons on a user interface — not the profits from the entire phone.

Apple, meanwhile, quotes Congress in saying that “it is the design that sells the article” and, because profits attributable to design are often “not apportionable,” it wants the Supreme Court to uphold the lower court ruling.

When lawyers from Apple and Samsung show up in Washington D.C. tomorrow, it will mark the first time the U.S. Supreme Court has heard a patent case in more than 120 years.