I am using Browsernizer gem to prevent some browsers version from accessing website and redirect to a static instruction page to upgrade browser version.

So using before_filter method in ApplicationController to detect browser version & redirect to a page. The problem is, without route, we can't call the before_filter method directly in my test case.

So, To fix this problem...

Create TestController in my_app/test/functional/application_controller_test.rb
Append test route to application
Setup @controller, @request objects [if required]

For Example:(Rails 4.1.14.2 & ruby-2.1.7)

my_app/Gemfile

source 'https://rubygems.org'
gem 'browsernizer'
group :test do gem 'test-unit','~>2.5.0'
end

my_app/app/controllers/application_controller.rb

class ApplicationController < ActionController::Base
 before_filter :other_filter_method
 before_filter :check_browser_support 

 def check_browser_support
  unless request.env['browsernizer']['supported']
      render :layout => browser_layout(params[:action]), :template => '/static/browser.html.erb'
  end
end  
private
def browser_layout(my_action)
    if my_action =='index'
      'my_browser'
    end
 end
end

my_app/test/functional/application_controller_test.rb

require 'test_helper'
class TestController < ApplicationController
  def index; end
end

class ApplicationControllerTest < ActionController::TestCase
 MyApp::Application.routes.append do
    controller :test do
      get 'test/index' => :index
    end
  end
  MyApp::Application.routes_reloader.reload!

 def setup
  @controller = TestController.new
  @request = ActionController::TestRequest.new
  @request.env['browsernizer'] = {}
  @request.env['browsernizer']['support'] = false
 end

 test "it should redirect to my_browser page" do
   params = {:action=> 'index' }
   get :index, params
   assert layout: my_browser
   assert_template 'static/browser.html.erb'
 end
end

Run your Test Case using command ...
ruby -I "lib:test" test/functional/application_controller_test.rb