I've a Black Magic Declink Mini Recorder Frame Grabber which supports minimum 720p as Video Input. But my camera has a VGA resolution which ostensibly will give output in 640*480 resolution. The card accepts both SDI/HDMI slots for Intput and Camera cable I have is currently having BNC Connector at it's end. Could someone suggest how can I use this Video Card to process VGA Video Output from my camera?
Your problem is not (only) resolution. 640x480 resolution VGA is analog video, so you need an analog -> digital video converter. This $200 Analog -> SDI Mini Converter from Blackmagic Design will do what you need.
Then again, for not much more than $200, you can get a camera that speaks HDMI and gives you true 720p.