This can be successfully achieved by placing the blame of such non-responsiveness on a shortfall in cell phone signal, end-of-life of current battery charge, accidental switching into vibrate/silent mode, and plethora of difficulties related to WiFi.
All aforementioned alibis have a nice ring-of-truth, and there is no way your mom, your annoying 16-year old sister, your friend Steve/Heather (who only calls to ask for a ride or to borrow cash or score some of your weed), or that creepy dude from last Thursday's party whom you FB-friended when you were too drunk, can prove otherwise.
Mom: Mijo, I kept calling last night. I made hígado encebollado, nopales con verdolagas and lentejas, just like we do every Tuesday.
You: Darn, mom, I can't believe I missed that awesome banquet. You know, it must've been when I placed the phone on vibrate earlier to go on PseudoCybernation from Steve. Sorry I couldn't get your call.
Mom: I tried to leave you a voice message, but your mailbox is full.
You: Yea, I know. Thing is, I'm waiting for Verizon to do away with their stupid limit of 25 voicemails, so I'm protesting by keeping my inbox full.
Your friend Steve: Hey bro, I txtd you last night man! These two honeys wanted to get down, but they live all the way down in San Ysidro. I was thinking maybe you could be designated driver since you're doing that Lent thing. Wha happen yo?
You: Aww, man! Really?? I was out all day doing errands with my lil sis for her Science Fair project, but I didn't have my car charger with me, so my Droid died ‘cause I was using it to GPS navigate around North Park, and the Google Maps App literally sucked the life out of the poor battery. I couldn't recharge until I got back from dropping her off at my parents'.
Your friend Steve: But dude, you're usually in and out of there like good weather in Indiana!
You: Yea man, but my mom begged me to try her Tuesday Special...
Your friend Steve: Oh snap! Is she still cooking that nasty liver with all that crazy green stuff?
You: ugh... don't remind me...