Question: I work remotely. I'm soon off abroad for a few months and will continue to work remotely while I'm away, taking the company laptop and possibly other similar hardware with me to perform my duties. The trip is my own choice.

My employer has asked if I could insure the hardware through my travel insurance, saying that he doubts the company policy will cover the USA (we're based in the UK).

As the hardware itself does not belong to me and is needed to fulfil my job (without any clauses covering insurance in my contract), is this something I can reasonably be expected to do?

Answer: 
You have a little bit outside the box problem here. 

1. You are voluntarily traveling, this is not for business, but yourself.
2. The company wants to minimize the obvious risk of losing their equipment while you are jetting around the world (their view, not yours)
3. Any insurance YOU buy is NOT going to cover something you do not own, period.

You need to have a conversation with your manager. Indicate that since the equipment belongs to the company and not yourself, you will be unable to obtain any insurance coverage for it on your own. If they would like to obtain additional coverage than what they normally carry, then you could have a discussion about having that additional expense reduced from your salary.

In summary this is how I see it.

1. You are voluntarily making this trip, it is not business related or directed.
2. The company owns the equipment though, so they need to make whatever arrangements they see fit.
3. You will have to decide if you can accept what they come up with or work out your own plan.

Additionally if you were to buy your own equipment and use it for work while traveling you would need to additionally indicate with the insurance company that you are using this equipment for work, they may reject a claim at some point if you did not indicate this.

This will NOT be travel insurance, that is for if you get sick etc. and have to cancel your trip. You need to look into a 'personal articles' policy (US terminology your local agent can help you determine the right UK coverage). This is insurance that covers a specific item. I have it on several computers, my wife's expensive jewelry and a few other items easily lost, damaged, or stolen.
TL;DR
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Yes, the employer can have good reasons and might request you for such additional insurance. However it's best to check all details first.

Full answer
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Let me address this question from a perspective of a person with some experience in insurance industry.

There are two factors to consider. In general you are usually liable for the property of your employer however this is usually limited to some degree. So if you leave your laptop in a car and it gets stolen you may be liable for its loss as this is in general something you should not do. On the other hand if you accidentally drop the laptop at your home it's usually insured and it the insurer takes a liability on this.

Yet the insurance has its limitations and details depends on the insurer's product and employers choice (and for large companies negotiations). If the company is based in UK and doesn't expect their employees to travel outside the country the company may buy an insurance limited to UK only (that in general will be cheaper). On the other hand they may as well have coverage for trips abroad, albeit it can be limited, e.g. to EU/Europe only or to business trips ordered by the employer only. As you can see both cases wouldn't apply if your laptop gets damaged in the US which essentially means the liability is on you then.

So yes, the employer might request you to additionally insure the laptop.

What I would suggest is to ask the employer to check details about the insurance coverage they have. They probably have some specific person responsible for that inside a company and/or a broker who is responsible for handling their insurances. Ask about two things - to check if your specific situation is covered and what should be the conditions of the insurance to match those normally covered cases. If it is covered you're clear and good to go.

If not, you should ask if it is possible to extend the insurance for the laptop and on what cost (to be covered by you as a reimbursement to your company, you'll probably need sign some extra agreement on it).

Then go to insurance company/agent and ask if it is possible to include such insurance. It can be already included (unlikely), an additionally paid extension or a separate insurance. If the insurer of your choice doesn't have such option, ask other insurers as well.

Now you have a clear situation and know the costs. It should be up to you to choose one, however check with your employer if they are happy with your choice of insurer. There may be some crappy companies as well and employer may say they won't accept such insurance.

Another approach is that you agree to cover the loss if the equipment is lost or damaged and it's not covered by the insurance. You have probably agreed to that already but if not then again - there should be some formal agreement. Now unless the agreement clearly says you are obliged to insure the equipment (two sides can agree on almost anything) it's up to your discretion if you look for some kind of insurance to cover that risk or you just accept the risk on yourself.