It may have changed, but in my day you sat the 11+ or whatever and if you passed you would automatically get in to the grammar school. Think tehre was an appeals process for those who didn't. Mind you, my school was weird and went on teacher recommendation, not the 11+, and started at 14, so not all areas are the same.
There are some v good grammars in Lincs and also some very good technology colleges and the like. Which area were you thinking of?
Aha you're looking for girls? Well i went to the girls grammar in grantham and it was jolly good - but that is some time ago. I would say though that you need to consider what you will do should your dds fail the 11+. In my day tbh the alternatives weren't all that great.
In my day (aged that I am) it was KGGS for girls and Kings for boys as the grammar options. Then Walton Girls - for girls which was classed as a secondary modern I think plus The Central School which was co-ed. Both of these were ok. Central in particular was improving a lot. Then there was St Hughs and St Wulrams i think - both of which were crap! (In the eyes of the outsider anyway) Out of Grantham there is Charles Read secondary Modern at Corby Glen - which was also pretty crap! Of course it may all be different now.... Definately one thing to also consider is that if you are going with the grammar schools then it will be single sex. Is that what you want?