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.
If it's a work trip (i.e. they are sending you) then it's their responsibility, if it's a personal trip it's reasonable to expect the employee to cover it.