deploy.rb

## Capistrano v3
# /config/deploy.rb

set :application, '<site_name>' #example.com
set :use_sudo, false
set :build_dir, "build"
set :ssh_login, "<login_details>" #root@example.com
set :deploy_dir, "/var/www/#{fetch(:application)}"

namespace :middleman do
  desc "Build and deploy middleman project"
  task :deploy do
    invoke 'middleman:build'
    invoke 'middleman:deploy'
  end

  desc "Run build utility"
  task :build do
    run_locally do
     execute "middleman build"
    end
  end

  desc "Deploy to VPS"
  task :deploy do
    run_locally do
     execute "scp -r #{fetch(:build_dir)} #{fetch(:ssh_login)}:#{fetch(:deploy_dir)}"
    end
  end
end

namespace :nginx do
  desc "Restart NGINX server"
  task :restart do
    run_locally do
     execute "ssh #{fetch(:ssh_login)} 'service nginx reload'"
    end
  end
end

after 'middleman:deploy', 'nginx:restart'

__END__

cap <stage> middleman:deploy

You'll likely need to setup SSH login with your VPS for this to work.
There are some additional Capistrano v3 setup details I left out, mainly
the setup of "stages" which Capistrano boilerplates for you when you run
`cap install`. 

This is not an elegant approach to using capistrano, in fact
it does not leverage the power of the tool in the least. However, for 
a deployment for something like Middleman, this worked well for me.