Sending files securely has been hard and will continue to be for the time being. First off, good on you for trying to explain to users that email is not really meant for file transfer. There are a variety of security issues with using email for sending sensitive docs, but you obviously know that already. Here are some options:

Client-side software- arguably the most secure since the encryption occurs "pre-internet." Assuming all users are able to install the software (many companies have strict policies on what can be installed) and have the "know-how" to use the software (i.e. they are computer-literate) then this can be a great option. There are freely available tools for this exact purpose (e.g. axcrypt). The downside, is you still have to figure out how to send the files. In your situation with the 15MB limit, this may not be the best solution.

Server-side software (self-managed)- people have mentioned ownCloud. This is definitely an option, but you either have to deal with installing it yourself or running it on a provider. Assuming you don't want to set it up yourself (you may not have the time, trust that you'll set it up correctly/securely, etc.), you are then relying on a third party to host it for you. In my opinion, at this point you are no better off (security-wise) than using a service that does it all for you (which leads me to the next option...).

Secure file service- there are a ton of providers in this area. Generally, how they work is your users upload a file, the provider stores it, and provides a URL for file download. Not all providers are equal- make sure they encrypt the files on their servers and not only during upload/download with HTTPS, also password protection is likely a feature you'll want, otherwise anyone with the link can download the file(s). I Googled "send files securely" and the first result looks like a good option, https://www.sendfilessecurely.com.

Best of luck!

@Breffni-Potter Right and no one is forcing you to use the site I mentioned. I’m not sure why you are so hung up on this. I listed multiple options. I mentioned that there are many similar services to choose from. I selected one that from a security perspective appears to be doing everything right (at least as much as one can expect from this type of service).
On the other hand, you said everything was encrypted on the site you mentioned, so I asked what that meant specifically. I assumed you might know since you know the guy. So far, I've heard nothing about it.

@Breffni-Potter The site I listed is as credible as any other site. At least they have contact info, details about their security (https://www.sendfilessecurely.com/technical-security-overview.aspx), where they are based/hosted (https://www.sendfilessecurely.com/where-are-files-stored.aspx), etc. I get that sites like the one you listed are going for the "minimalistic" look and feel, but come on... no contact info, no details, just a statement that they are fast, easy, and secure.

@Breffni-Potter What do you mean "everything is encrypted?" That site provides zero details. Do you mean they use HTTPS? They encrypt in storage? If so, what type of encryption? What about the keys? etc. It's a pet-peeve of mine when I see something claim it's "secure" without any explanation. I've seen many of these services buy a $10 SSL cert and then claim they are encrypted and therefore secure.

Sending files securely has been hard and will continue to be for the time being. First off, good on you for trying to explain to users that email is not really meant for file transfer. There are a variety of security issues with using email for sending sensitive docs, but you obviously know that already. Here are some options:

Client-side software- arguably the most secure since the encryption occurs "pre-internet." Assuming all users are able to install the software (many companies have strict policies on what can be installed) and have the "know-how" to use the software (i.e. they are computer-literate) then this can be a great option. There are freely available tools for this exact purpose (e.g. axcrypt). The downside, is you still have to figure out how to send the files. In your situation with the 15MB limit, this may not be the best solution.

Server-side software (self-managed)- people have mentioned ownCloud. This is definitely an option, but you either have to deal with installing it yourself or running it on a provider. Assuming you don't want to set it up yourself (you may not have the time, trust that you'll set it up correctly/securely, etc.), you are then relying on a third party to host it for you. In my opinion, at this point you are no better off (security-wise) than using a service that does it all for you (which leads me to the next option...).

Secure file service- there are a ton of providers in this area. Generally, how they work is your users upload a file, the provider stores it, and provides a URL for file download. Not all providers are equal- make sure they encrypt the files on their servers and not only during upload/download with HTTPS, also password protection is likely a feature you'll want, otherwise anyone with the link can download the file(s). I Googled "send files securely" and the first result looks like a good option, https://www.sendfilessecurely.com.

Best of luck!