My question is this; Above Landlord Insurance, is it recommended to also carry an umbrella policy?  

Look at an umbrella for an additional $2-5 million of liability

I've got an umbrella policy, etc. so I'm not worried as much on the liability side.  

I’d put the house in an LLC, get a $1m umbrella policy ($300 for the year) and ensure it covers the pond.

Get a generous umbrella liability policy that easily covers your assets.

to address your liability, you buy an umbrella policy with large coverage, say $5M.

I don't have children and am a huge dog - guy and pretty much allow all my tenants to have dogs... even PITBULLS which are so prevalent down here, I have extra umbrella insurance to cover this precise breed.So, it's 3/8 and I haven't heard from them... the non-touchy feely one texted me Saturday and said she's been busy and doesn't take well to threats or demands, which is the line I used on them when they started barking orders at me.   

Keep it in your name, insure it, and add a large umbrella insurance policy for yourself off your personal homeowners policy.

Just make sure you have $300,000 or more liability on each house and a $1 million umbrellas policy. 

@Aaron K. and @Claire Rosenberg all properties are in a flood zone the only differentiator with the flood zones is the "high-risk" flood zones is your lender will require flood insurance in order to get the funds.This is a law.These flood zones are identified with a Flood zone A, Flood zone AE or V, VE.Lenders do not need to require flood insurance in low-to-moderate risk flood zones usually identified as an X flood zone.It doesn't mean that the property will not flood it just simply means that you will not be "required by your lender" to purchase a flood insurance policy.Every year 20% and in some estimates 35% of flooding events are in the "considered low risk" flood zones.The purpose of all insurance (including flood) is to off set your risk this is why you buy a hazard (or homeowners policy) or umbrella policy or auto policy and of course life insurance.But flood insurance is the one that most people decided that they do not need, and many think that their homeowner policy will cover flooding.