I had lost my passport 4 years back, I was on an F1 visa then.
After receiving the new passport from Chicago I visited India where I had already scheduled a visa interview, thus I got the new passport stamped.
I had to show a copy of the police report that I had filed for the loss of documents, copy of the old passport, copy of old I-94s, letters from university/advisor etc. and I-20 (which is equivalent to I-129 for H1Bs). I also carried bank statements, copy of my lease, driver's license etc. to establish the case more, though the consular hardly looked at anything, just advised me not to lose the passport again. Actually if you lose the passport a second time, it is going to be very difficult to get a new one issued.