From a responsive website design agency, you should expect a fully mobile-friendly and cross-device optimized website that works smoothly on desktops, tablets, and smartphones. They should provide a modern UI/UX design focused on user experience and easy navigation. A professional agency will ensure fast loading speed, clean coding, and SEO-friendly structure. You can also expect them to test your website across different browsers and screen sizes for consistency. Additionally, they should offer customization options based on your brand identity and business goals. Finally, ongoing support and maintenance are important to keep the website updated and fully responsive over time.