Sorry to hear the sad news. Crime happening to our guests must be high on the list of every homeowner's nightmares. At least no one was injured; tthings can always be replaced. Hopefully it's an isolated event.
So,:"How do we handle this?" I'll start by pointing out the one thing you should NOT do. Do NOT fail to do whatever you can to handle this, meaning to help your guests. Stay on the scene of the crime, so to speak.
1) Seek calm. Take a deep breath, or 5 or 10. If you're a nervous wreck, it is certainly understandable. But now is actually a critical time to take action.
2) If you're sorry it happened and wish it hadn't, say so.
Listen carefully for what they are thinking and feeling. Be as honest and "Human" with them as you can, but try and keep things moving in a positive direction. No amount of tooth-grinding or lamentaion or ulcers will bring back their stuff. So, focus on what you CAN do.
3) Offer them all possible assistance (within reason)..Ask if they lost any medication or other items needing quick replacement. These are lawsuit happy times, so it might be wise to let them know (ONLY if true) that "nothing like this has ever happeded before."
4) Explain to them that your insurance doesn't cover their loss through theft. That is useful information to them. (Losses from theft of guests/renters stuff is almost NEVER covered under a Homeowner's policy, so it's not like you have done anything wrong that way.)
Ask if they have happen to have travel insurance. Sometimes American Express or a motorist's club- like AAA in the USA-- offer coverage under certain conditions. To be clear: it is THEIR job, and not yours, to handle any insuranc due. Just reassure them that you will be available to answer any questions, etc., should that arise in the course of filing the claim.
5) Offer to help them obtain a police report, which would be useful if they are covered by some kind of travelers' insurance. It also might be a wise move on your part, preventively speaking. It would be a shame if the police never knew the crime had happened.
6) If they no longer feel comfortable in the place, cheerfully offer them a pro rata refund. You want to make it clear you are on their side.
7) However: things are not always as they seem. If they try to squeeze you for money with threats, hysterics, etc., that's a HUGE red flag. As you know, there are ALL kinds of people out there, and a possiibility does exist that this is an "inside job." (Not a likelihood, simply a possib.) (Of course, they might bear the same suspicion about you. No reason for offense, necessarily. It's a "Human" thing. That would be part of the reason it's important to help build a bond at this point.
I hope that you find any of the above helpful. May the larger part of this sort of stressful drama be behind you.
I also have s ecurity system in our rentals that alerts me as well as the police, It is not only a deterant for thieves but a relief in todays times for vacationers feeling secure.
Put yourself in their shoes think like a vacation renter for a moment, realize that they feel violated to the core and somewhat fearful. It is our responsiblity as owners to do everything in our power to help them overcome all that we can.
You are only human and can only do so much, but let the semsitive side show thru for them they wiil not only appreciate the genuine feelings you show but the time and effort you put into your responses to them.
Good luck and may this never happen again.