The best insurance is to maximise the amount of time available to connect; travel to the connection point the day before if necessary.

Most travel insurance policies would likely not cover you if you are self-connecting.
EU261/2004 says nothing about the impact on a second ticket if a problem occurs with a first ticket - so while you may eventually be able to get some compensation and remedies based on delays to the first ticket [and you would probably have to fight this tooth and nail for months after the fact], you would still end up having to buy a new, second ticket on the day of travel, at your own expense, with no come-back as regards the second ticket. It is your responsibility to present yourself for each ticket in time for boarding. A delay on the first ticket may mean you eventually get EU261/2004 benefits for the first journey - but you have totally missed your second ticket and therefore lose all rights to that second ticket.

There is one online travel agency that I know of - kiwi.com, formerly Skypicker - that have a missed connections guarantee for self-connecting itineraries that they sell their customers - however, in case of any delay/cancellation, you must contact them as soon as possible, and follow all of their procedures to the letter of the law and they will rebook you to get you to your destination. You can read the relevant terms here. I have no direct experience of this agency, but I imagine that contacting them may be difficult and expensive if you are already midway through your journey, so how useful this guarantee turns out to be may not be as immediately good as it looks.