What is the ruling of the Sharia regarding an oath I swore before the judge concerning the estimation of the value of stolen gold, given that I do not know its true value precisely because years have passed since its theft?

It is not permissible for a Muslim to swear an oath concerning something of which he is not certain. The prohibition becomes even more severe if it leads to usurping another's right. The Prophet (peace and blessings be upon him) said: "Whoever swears an oath by which he wrongfully appropriates the property of a Muslim, he is a wicked person in it, and will meet Allah while He is angry with him." Then he recited the words of Allah Almighty: “Indeed, those who exchange the covenant of Allah and their oaths for a small price – those will have no share in the Hereafter, and Allah will not speak to them or look at them on the Day of Resurrection, nor will He purify them; and they will have a painful punishment.” [Quran, Al ‘Imran: 77].

If you swore an oath about the value of stolen goods that exceeded their true value, then you must make sincere repentance and return the excess amount to the person from whom it was taken. A Muslim should choose to bear loss in this world to avoid loss in his religion.