While some Mexican cities, namely those along the Mexican-United States border, have garnered a rather negative reputation, Guanajuato is an extremely safe city. So, the rule of thumb is basically just use your common sense and you'll be fine. For example, don't count out your life savings on a park bench, hang around dark dodgy-looking alleys or leave your camera lying out on an outdoor café table.
Keep an eye on your belongings in crowded areas (markets, buses, etc.) and tourist hot spots. While you don't have to worry about any major crime, being pickpocketed sure can put a dampener on your trip- so just be careful! Leave your valuables back at the hotel locked in the hotel safe or in your locked suitcase. Carry around a copy of your passport instead of the real thing, and don't carry around more cash on you than you need.
In the event that your credit card has been unfortunately lost or stolen, you can call the following toll-free phone numbers: