GEOMET, INC. Amendment No. 1 To 2006 Long-Term Incentive Plan

Exhibit 10.12

GEOMET, INC.

Amendment No. 1

To

2006 Long-Term Incentive Plan

THIS AMENDMENT NO. 1 (this “Amendment”) to the 2006 Long-Term Incentive Plan (the “Plan”), of GEOMET, INC., a Delaware corporation (the “Company”), originally adopted effective April 17, 2006, is herein adopted effective March 13, 2007;

WHEREAS, the Board of Directors of the Company has approved non-material amendments to the Plan to provide that “Fair Market Value” as defined thereunder shall be based upon the closing price (rather than the average of the highest and lowest selling prices) of a share of the Company’s Common Stock and to provide that “Corporate Change” as defined thereunder shall not include private offerings of the Company’s Common Stock;

NOW, THEREFORE, the Plan shall be amended as follows:

1. Defined Terms. Capitalized terms used but not defined herein shall have the meanings given such terms in the Plan.

2. Amendment. Section 2.11 and Section 2.16 of the Plan are hereby amended in their entirety so that, as amended, said Sections 2.11 and 2.16 shall read as follows:

“2.11 “Corporate Change” means (a) the dissolution or liquidation of GeoMet; (b) a reorganization, merger or consolidation of GeoMet with one or more corporations (other than a merger or consolidation effecting a reincorporation of GeoMet in another state or any other merger or consolidation in which the stockholders of the surviving corporation and their proportionate interests therein immediately after the merger or consolidation are substantially identical to the stockholders of GeoMet and their proportionate interests therein immediately prior to the merger or consolidation) (collectively, a “Corporate Change Merger”); (c) the sale of all or substantially all of the assets of the Company; or (d) the occurrence of a Change in Control. Notwithstanding the foregoing, “Corporate Change” shall not include the Offering or any public offering of equity of GeoMet pursuant to a registration that is effective under the Securities Act or any private offering of equity of GeoMet pursuant to an exemption from the Securities Act. A “Change in Control” shall be deemed to have occurred if (a) individuals who were directors of GeoMet immediately prior to a Control Transaction shall cease, within two years of such Control Transaction to constitute a majority of the Board (or of the Board of Directors of any successor to GeoMet or to a company which has acquired all or substantially all its assets) other than by reason of an increase in the size of the membership of the applicable Board that is approved by at least a majority of the

individuals who were directors of GeoMet immediately prior to such Control Transaction or (b) any entity, person or Group acquires shares of GeoMet in a transaction or series of transactions that result in such entity, person or Group directly or indirectly owning beneficially 50% or more of the outstanding shares of Common Stock. As used herein, “Control Transaction” means (a) any tender offer for or acquisition of capital stock of GeoMet pursuant to which any person, entity, or Group directly or indirectly acquires beneficial ownership of 20% or more of the outstanding shares of Common Stock; (b) any Corporate Change Merger of GeoMet; (c) any contested election of directors of GeoMet; or (d) any combination of the foregoing, any one of which results in a change in voting power sufficient to elect a majority of the Board. As used herein, “Group” means persons who act “in concert” as described in Sections 13(d)(3) and/or 14(d)(2) of the Exchange Act.”

“2.16 “Fair Market Value” means (a) for so long as the Common Stock is listed on the NASDAQ Global Market or other exchange or association on which the Common Stock is traded, the closing price for such stock as quoted on such exchange for the date the Award is granted (or if there are no sales for such date of grant, then for the last preceding business day on which there were sales), (b) if the Common Stock is traded in the over-the-counter market, the closing price as reported by NASDAQ on for the date the Award is granted (or if there was no quoted price for such date of grant, then for the last preceding business day on which there was a quoted price), or (c) if the Common Stock is not reported or quoted by any such organization, fair market value of the Common Stock as determined in good faith by the Committee using a “reasonable application of a reasonable valuation method” within the meaning Section 409A of the Code and the regulations thereunder. Notwithstanding the foregoing, “Fair Market Value” with respect to an Incentive Stock Option shall mean fair market value as determined in good faith by the Committee within the meaning of Section 422 of the Code.”

3. Nature of Amendment. In accordance with Section 14.1 of the Plan, the Board has determined that this Amendment shall not require approval of the shareholders of the Company and therefore this Amendment shall become effective as of the date that the Board has approved this Amendment, as shown below.

4. Ratification. As amended hereby, the Plan in hereby ratified and confirmed.

IN WITNESS WHEREOF, this Amendment has been executed on behalf of the Company by authority of the Board of Directors as of March 13, 2007.

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