I know that the Declaration of Independence is generally not considered law, per se. But have its principles ever been cited in the reasoning for a ruling?
The Declaration of Independence is often cited (along with the Federalist Papers) when the court is attempting to justify a particular interpretation of The Constitution by looking at the intent of the drafters.
For example, in Arizona State Legislature v. Arizona Independent Redistricting Commission 576 U.S. ____ (2015), in establishing that the people have ultimate sovereignty quoted the Declaration of Independence:
Governments are instituted among Men, deriving their just powers from the consent of the governed...
Following that (after also quoting some text from the Constitution), Justice Ginsberg concludes:
In this light, it would be perverse to interpret the term “Legislature” in the Elections Clause so as to exclude lawmaking by the people, particularly where such lawmaking is intended to check legislators’ ability to choose the district lines they run in...
As a second example, Justice Scalia, in his dissent in Obergefell v. Hodges 576 U.S. ___ (2015), refers to the Declaration of Independence:
This practice of constitutional revision by an unelected committee of nine, always accompanied (as it is today) by extravagant praise of liberty, robs the People of the most important liberty they asserted in the Declaration of Independence and won in the Revolution of 1776: the freedom to govern themselves.