I’m not exactly sure how to best charge for updating a clients site. I have an hourly rate but when they contact me with tiny updates and changes here and there, I’m not quite sure how to best charge for that. Should I just do so on 30min increments? Should I charge a minimum of 1hr for any updates they request? I suppose there are many options but I’m open to any suggestions.
If they are contacting you quite regularly for little updates you should be charging for all your time.
Even though it may only take 30 mins to do the work they ask, all the correspondence, contacting the client, reading what they have sent you and all that other miscellaneous stuff is probably doubling that 30 mins.
Bottom line, I would say charge per hour with a minimum of 1 hour.
You could always charge for an hour and then calculate the collective amount of time required for all the small tasks and once the hour’s worth is used up then charge for the next hour (kind of like putting the services on a pre-paid “tab” which can be re-couped over sequential sessions) 
Since you don’t want your client sending you one tiny change one minute, you take time away from a project and fix it, then another hour later get another tiny change, etc. To avoid this it’s best to have a minimum hour rate. Personally I use a 1 hour minimum for any updates and then bill in 15 minute increments after that.