Hamburg - Restaurants

I am not quite sure what you mean with "romantic", but my recommendation for a restaurant with typical local atmosphere and refined regional cuisine would be Old Commercial Room:

http://www.oldcommercialroom.de

Another restaurant which is very atmospheric would be Cölln's Austernstuben:

http://www.coellns-restaurant.de

My suggestions would be (not in order of romance factor, that to a large extent depends on the company and what your taste):

High-end stuff:

1. Jacob's Restaurant
Currently the highest rated restaurant in Hamburg (and has been for a while), an institution in the posh Elbe suburb of Blankenese, top-notch cuisine with a wine list to match, views of the river and a fabulous terrace with linden trees.
http://www.hotel-jacob.de/index.php?id=123&L=1

2. Poletto
Cornelia Poletto serves Michelin starred italian influenced cuisine in an unassuming little restaurant in the nice (and relatively central residential neighbourhood of Eppendorf. Gracious service, the interior a bit austere, but low ceilings create certain intimacy. Across the street is a small park bordering one of the Alster canals where you could go for a stroll.
http://www.poletto-restaurant.de/

3. Tafelhaus
Very modern interiors, high-end food, not intimate, but with spectacular views of the port and you could afterwards go for a stroll along Strandweg in Neumuehlen/Oevelgoenne, lined by small captain's houses with river views.
http://www.tafelhaus.de/

4. Prinz Frederik
Often overlooked, and it's been a while since I have been, but it still gets great reviews. Very conservative, very intimate, only around 20 seats. In a small Relais & Chateaux hotels housed in a period mansion in one of the posher inner-city residential streets. A reasonably short stroll from the Outer Alster for star-gazing afterwards (and everything in Hamburg has to be related to water anyway).
http://www.abtei-hotel.de/index2.html

5. Piment
Wahabi Nouri has just been named German chef of the year by the Gault Millau guide. He has been producing excellent cuisine employing spicy influences from his ancestral Morocco in a small restaurant seating only around 25 people amidst its dark red couloured walls in the nice Eppendorf district.
http://www.restaurant-piment.de/

Not starred, but charming

1. Witthues
Slightly old fashioned atmosphere in a reet-roofed building in the deer park in Blankenese. Older clientele during the day, a bit younger in the evenings, not hip, though.
http://www.witthues.com/

2. Schweizweit
A small basement restaurant specialising in cheese fondue in the diverse neighbourhood of Altona. Cheap and cheap interiors. Nothing specatcular at all, but intimate. Just to provide a really cheap alternative, basically.
http://www.schweizweit.de/

That said and without offence intended, Old Commercial Room doesn't come to my mind instantly when romance is called for. I find it a bit touristy, to be honest.

Thank you - It was Witthues that I visited for afternoon tea a few weeks ago and on the journey back to the centre of Hamburg we passed several establishments that seemed to look very pretty and quaint i.e romantic but possibly they may not be that good.