How to insure my belongings in the event of theft internationally?

I've taken a look at some traveler's insurance, but none of the policies seem to do exactly what I want. I have been robbed multiple times while abroad and obviously it's always a pretty big financial burden. I'm going to be in Mexico City in a few weeks and will be staying in a pretty cheap hotel with a laptop, iPad, iPhone, passport etc. Is there any way to financially protect myself in case any of that gets stolen?

I suggest that you stay at a nicer hotel, like Holiday Inn, any 4 star or higher hotel will do. It's going to be cheaper than the insurance and they have a safety deposit box for your valuables.

Take a light but strong chain 10 foot. Buy a good padlock for your suitcase. Chain suitcase to what is in room? Keep passport and money in hotel safe. Take a certified photo copy of it with you on the street. That usually does it. Have a hardcase suitcase as well. Hotel thief's are usually snatch and go. They do not like to spend time and noise. It also lets you chain your door shut at night. And I have traveled the world and stayed at hotels that will scare you. Never travel with out 10 foot of light strong chain. You will need order the chain not store bought but industrial chain. Case hardened or Titanium like mine is. Some cable is also good case hardened cable.

Keep them with you at all times