i would encourage the tenant to get insurance, many think your policy covers them, make sure they are aware that they have to buy there own coverage. I do know of a situation where the landlord paid for the insurance policy out of the rent to make sure it was always in force.
If you are worried about your liability limits - talk to your insurance broker about getting an Umbrella policy - that way you are covered for a number of properties for a rather minimal charge, and you can increase your liability limit up to $2 million or $5 million.
One of the benefits of having your tenant have insurance is in the event of a fire, your tenant smokes and doesn`t put out his cigarette, or puts it out in the planter with peat moss. It is nice for your company to be able to go after the tenants insurance for the damages - that way you have no claim on your policy.
Again always take the time to read your wordings, andif it is to much, always read what is excluded and what is limited.
Also another insurance tip, make sure you contact your broker every year to review your renewal - make sure you have adequate coverage in place, and for those of you who own homes, make sure you ask them to reevaluate your homes to make sure they are insured to the proper value. Many companies are now offering guaranteed replacement cost coverage on rentals if you meet the criteria, again check with your broker to see if your homes fit, or if another company offers that coverage. This is important especially in todays markets with rising costs.
Older homes should carry some sort of bylaws coverage - again protect your self in the event of a loss.