api.rb

require 'sinatra_authentication'

class Api < Sinatra::Base
  register ::MyApp::Sinatra::Authentication
  
  get '/api/ping' do
    render "Authentication successful"
  end
end

sinatra_authentication.rb

module MyApp
  module Sinatra
    module Authentication
      def self.registered(app)
        app.before do
          content_type :json
          authenticate if api_request?
        end
        app.helpers Helpers
      end

      module Helpers
        def api_request?
          request.path_info.match %r{^/api/}i
        end

        def authenticate
          unless authenticated?
            response['WWW-Authenticate'] = %(Basic realm="API")
            throw(:halt, error('Unauthorized', 401))
          end
        end

        def authenticated?
          auth = Rack::Auth::Basic::Request.new(request.env)
          auth.provided? && auth.basic? &&
            auth.credentials && @current_user = ::User.authenticate(*auth.credentials)
        end

        def current_user
          @current_user
        end

        def render(output, code = 200)
          out = { :response => output }.to_json + "\n"
          [code.to_i, out]
        end

        def error(output = 'ERROR', code = 400)
          render(output, code)
        end
      end
    end
  end
end

user.rb

class User < ActiveRecord::Base
  acts_as_authentic

  def self.authenticate(username, password)
    c = find_by_username(username)
    c && c.valid_password?(password) ? c : nil
  end
end