New masking tape?

It may peel off the paint though. You don't want tape that's going to be too harsh and ruin the kit. I use Frog yellow painter tape or Tamiya tape.

Types spring to mind, 

Non-sticky thick white PTFE tape used to gas seal threaded pipes, but pretty much useless for anything else.

Other 'self-sticking' tape permanently bonds to itself & anything else, used to waterproof/repair leaks, etc, wouldn't use except for its' intended use.

I use Tamiya Masking tape for masking, it works, doesn't leave residue, & is easy to get.

I prefer Tamiya also, but there are narrower sizes I like that Tamiya doesn't make.  Both Pactra and Testors make a 1/16th width.  Also, I keep some blue 3M low tack masking tape in a very wide (I think it is 1 1/2 or 2 inch) for very large area masking.  I do the edge with the Tamiya, then bridge from the tamiya to the large area with the 3M, because I find the tamiya gives a crisper edge.

Exactly as Don said. 

I dont buy narrow-sized masking tape anymore.  I just lay out the standard width Tamiya tape on a clean cutting mat and use a steel ruler and sharp knife to cut custom narrow widths.