<p>Is there a way to access Visual Studio's built-in ASP.NET Development Server over HTTPS?</p>

Cassini does not support HTTPS.
However, you can use IIS to do this, if your using IIS 5.1, download the MS IIS toolpack for IIS 6.0, it comes with a tool to create self signed SSL certificates. This works on IIS 5.1
http://www.microsoft.com/downloads/details.aspx?FamilyID=56fc92ee-a71a-4c73-b628-ade629c89499&DisplayLang=en
The one tool you need (SelfSSL.exe) works just fine with IIS 5.1. Unfortunately, it comes bundled with a bunch of other stuff.
Steps:
Install the IIS Tools File. If you want, you can click Custom and tell it to only install SelfSSL.
Activate the site in IIS that you want to install a SSL certificate too.
Go to Start / Programs / IIS Resources / SelfSSL
This will launch a command prompt in the SelfSSL directory.
Using the provided help, run SelfSSL. The command I used was: selfssl.exe /N:cn=[MACHINENAME] /K:1024 /V:90 
/S:5 /P:443
The /S switch indicates which site to install the certificate. You can figure out the number by looking at your sites in IIS and counting (Starting at 1 for the first site, not 0), to the site you want.
Once this has ran, browse to your localhost over HTTPS
You should receive an error message stating that this certificate is from a untrusted source. You can either add your machinename to the browsers “Trusted Authorities” list, or you can tell the browser to ignore this.
At this point, you will be able to run your localhost over HTTPS.