Use Jbuilder within Sinatra.

app.rb

# coding: utf-8

require "bundler"
Bundler.require

helpers do
  def current_user
    @current_user ||=
      Hashie::Mash.new(admin?: [true, false].sample)
  end
  def edit_article_url(article)
    "http://example.com/articles/#{article.id}/edit"
  end
  def author_url(author)
    "http://example.com/authors/#{author.id}"
  end
end

get '/' do
  @article = Hashie::Mash.new(id: 1, name: "DRAGONBUSTER02", published_at:"2012-01-10")
  @article.author = Hashie::Mash.new(id: 1, name: "Mizuhito Akiyama")
  @article.comments = Array.new(1) { |i| Hashie::Mash.new(id: i+1, name: "@ikm", content: "My missing book...") }

  jbuilder :index
end

Gemfile

source "https://rubygems.org"

gem "sinatra"
gem "tilt-jbuilder", ">= 0.4.0", :require => "sinatra/jbuilder"

gem "hashie"

index.jbuilder

# Place this file in the `views` directory.

json.(@article, :id, :name, :published_at)
json.edit_url edit_article_url(@article) if current_user.admin?

json.author do |json|
  json.(@article.author, :id, :name)
  json.url author_url(@article.author)
end

json.comments @article.comments do |json, comment|
  json.(comment , :id, :name, :content)
end

Make sure you're requiring sinatra/jbuilder. Then, in views/index.jbuilder things work as expected.
In my example below, I'm skipping options with a {} and passing in local data

require "sinatra"
require 'sinatra/jbuilder'

get '/movies/:id' do
  jbuilder(:index, {}, flick: Flick.movie(params[:id]))
end

I learned this from the tilt docs