I don't actually have experience with silverlight, but for this question in general there are a grabbag of OK options. Most of us still tend to rely on trial&error + hunch.
LoadRunner is kinda the grandaddy but if you have to ask its out of your budget.
Keynote has a tool called KITE that is a free download. You start it up, and then within it you start an IE browser, do whatever you think a user would do, and then save the recorded session as a script. You can then upload that script to their network of servers and pay them to run it rapid fire. They'll also work to get you on the hook to pay them to help you write the scripts. They're an "enterprise-y" vendor that way so it takes budget to really get a solution in place.
Gomez has a similar service, I don't know the details as well. Its a little more utility-rate oriented in that you buy by the transactions in bulk. They can be cheaper but again be in a "thousands" mindset.
Selenium is a free/open-source tool that can be used similar to KITE, but you have to rig the clustering/clients/reporting stuff up. One of the developers also runs Browser Mob which will basically run your selenium scripts on their load servers for you for cheap.
Those can all be good for even complex ajax apps, but I honestly don't know enough about silverlight to say if they'd even work.
Like I said up front, most of us still wing it. Setup very careful monitoring and metrics collection as early as you can, and trend as users adopt the system. Start to develop rough ratio metrics for how many users can be active at once per cpu or per GB of memory or correlates to how many sql requests/second, etc. This helps you project your user capacity, shows you what your top hogs are, and shows you when all of a sudden a metric spikes the chart because of a change you made.