Modern technology has unfortunately helped us in many ways and hindered our communication skills in others. If you cannot reach the person directly by phone or mail, or if for some reason you simply do not want to do it that way, this is an alternative. If you are truly sincere in your tone and words, you have nothing to fear or worry about. Many voice mails can go much longer, but some have 30-60 second maximums. You can always call right back and record the rest of your message, but this is where being succinct and friendly in tone is of great importance if you want your message to be well taken.
Cards can be very nice.
The addition of a gift is optional and situational. True, it is the thought that counts, but when it is a loved one involved, think abit bigger than usual, and make it special. If it is a business associate or friend, a gift is really optional and probably overkill. Taking them to dinner or lunch would be a better idea if possible. You will be respected by the person you are addressing as well as by yourself more if you are able and willing to make your apology in this manner.